Operating under Commander Caribbean Sea Frontier during her time off the island (12–16 July), Davis and her squadron-mates performed a deterrent mission, preventing neighboring nations from interfering in the internal affairs of Haiti during President Francois Duvalier's recovery from a heart attack.

Subsequently, wrote one squadron chronicler, none of DesRon 12's ships operated together again in 1960, although Davis and USS Harlan R. Dickson proceeded into the Black Sea "on a special assignment," the third and fourth U.S. warships to enter that body of water since World War II.

Davis and DesRon 12 departed Pollensa Bay and the Sixth Fleet for Rota, Spain, and thence, to the continental United States on 13 February 1961, and reached their home port eleven days later to begin leave periods and pre-yard tender availabilities.

In July, she received word that she had won gunnery and supply department “E”s for 1962, as well as her third consecutive Battle Efficiency “E.” During that deployment, Davis and her squadron mates "participated in Operation Full Swing, MidLandEx and RegEx 62...commended at varying times for signal bridge work to their fine shooting, from smart seamanship to the spreading of good will ashore.

Returning to Newport on 29 November 1962, Davis put to sea as part of the holiday ready-duty ASW task group, steaming to Bermuda and operating with antisubmarine warfare support carrier USS Wasp over Christmas.

After conducting ASW evolutions (28 January – 9 February), followed by an upkeep period at Newport, Davis operated with Task Group Bravo as it covered the visit of President John F. Kennedy to Costa Rica in March, remaining with Wasp and in company with Compton and Gainard.

Subsequently, Davis sailed on 4 June 1963 with 26 Naval Reserve Officers Training Corps midshipmen on board, as Task Group Bravo began a six-week cruise, beginning with visiting a succession of Gulf Coast ports, Galveston and Houston, Texas, Mobile, Alabama, Gulfport, Mississippi, Port Arthur, Texas and New Orleans, Louisiana, proceeding thence to La Ceiba and Puerto Cortés, Honduras, Santo Domingo, Curaçao, Montego Bay and Kingston, Jamaica, San Juan and Ponce, Puerto Rico.

Illustrative of the nature of the routine Davis often followed, on 24 May 1966 she fired 13 rounds of gunfire support during the afternoon watch, then stationed the special sea and refueling detail at 21:58 as she began maneuvering to go alongside the underway replenishment ship Sacramento.

Davis sailed from her home port on 22 September 1966 for Boston Naval Shipyard, arriving there the following day for "extensive work on her engineering plant," after which she returned to DesRon 12 for active operations on 26 November.

At 17:19, however, Davis and Massey received verbal orders to proceed at once to the assistance of the technical research ship Liberty, that had, earlier that day, been attacked in international waters by Israeli jets and motor torpedo boats, approximately 15 miles (24 km) north of the Sinai port of Arish, UAR.

Then, following visits to Porto Contini, Sardinia, Golfe-Juan, France and Ibiza, Spain, interludes interspersed with operations at sea, Davis picked up a sonar contact on 24 August and evaluated it as a Soviet submarine.

Destroyers Massey and Basilone and escort ships Brumby and Lester, joined to assist, while the anti-submarine controllers on board Davis and Fred T. Berry conducted over 1,200 Magnetic Anomaly Detection verification runs on the submarine, utilizing aircraft from Essex.

Returning to Newport, the ship prepared for her next stint of operations at sea, and during that time served as the venue (3 November) for the ceremony in which Captain Leahy received the Navy Commendation Medal for his leadership in the evolutions that led to the 105-hour hold-down, and consequent surfacing, of the Soviet Foxtrot class submarine in August 1967.

A slate of ASW and AAW exercises, shore bombardment drills off Culebra and a "tough and exacting Operational Readiness Inspection" then followed, punctuated by four visits to San Juan and one to St. Thomas for recreation.

During her first gunline tour of that deployment, Davis, ComDesRon 36 and his staff receiving gunfire support briefings at Da Mang and Dong Ha Combat Base on 10 October 1968, operated off the northern coast of South Vietnam, just below the Vietnamese Demilitarized Zone (DMZ).

With Captain Murphy's relief as CTU 70.8.1 by ComDesRon 5 on 6 January 1969 upon the conclusion of Valiant Hunt, Davis conducted a succession of rest and recreation visits, to Kaohsiung; Cebu, Philippines; and Subic Bay.

After taking on supplies, fuel, and stores at Norfolk Naval Base (19–21 January), the ship got underway for Port Everglades, where she conducted "pre-weapon system accuracy test alignment and calibration checks.

Standing out of her home port on 25 June, she returned to Boston on 1 July to wrap up her ASW modernization, yard workers toiling on projects that ranged from major boiler work to the installation of variable depth sonar (VDS) and AN/WSA-1C and a secure voice system, as well as modifications that would allow the ship to have a vertical replenishment capability.

Arriving at Guantanamo on 14 January, however, she hastily refueled and stood out, returning to sea for another stint of "special operations," occasioned by the report by the small Panamanian-flag motorship Johnny Express that she had been fired upon off the eastern tip of Cuba in mid-December 1971, and that a Cuban gunboat had attempted a boarding.

Underway on 28 April, Davis, along with other Newport-based ships, participated in LantReadEx 4-7, then put back into her home port on 10 May after a rough passage "with high winds and heavy seas being the rule," and continued preparations for sailing for the Mediterrnanean.

Davis and guided missile frigate Dewey departed Newport on 4 June 1972, rendezvoused with America off Cape Henry, Virginia, and set course for the Philippines; six days later, Admital Elmo Zumwalt, the Chief of Naval Operations, sent a message to the Vietnam-bound ships.

While in port, however, the ship's sounding and security patrol found water in compartment 3-44-4-E. After the de-watering process, investigation revealed a defective fire plug; damage to the sonar equipment resulted in its being left behind for repairs when Davis returned to the gunline on 25 August.

"Chopping" to TU 77.1.2 to participate in Operation Linebacker, Davis pounded targets along the coast of North Vietnam over ensuing days, taking hostile fire upon occasion, the closest rounds splashing 50 yards (46 m) from the ship.

She resumed Linebacker raids as a unit of TU 77.1.1 on 12 October, carrying out nightly shelling and maintaining surveillance of merchantmen from the People's Republic of China lying off Hon La and standing ready to prevent any cargoes from reaching the beach.

On 15 October, Davis conducted the first of several operations wherein she launched air-filled plastic bags that contained "mini-radios" that "when winds and tides permitted, floated ashore to enable the North Vietnamese people to hear non-Communist radio programming.

Following sea trials (24 April), Davis underwent her nuclear weapons inspection (3–4 May), then a series of Operational Propulsion Plan Examination (OPPE) evolutions (13–14 May, 19–21 May and 27–28 May), before she carried out preparations for her next deployment (29 May – 30 June).

Departing her home port on 12 June, the ship operated as part of the Nimitz Battle Group in ComPTUEx 2-81, conducting extensive ASW and AAW exercises during that time, after which she enjoyed rest and recreation at Frederiksted, U.S. Virgin Islands.

Proceeding thence for the Suez Canal, Davis, accompanied by Voge, prepared for trouble in the wake of the recent signing of an accord between Libya, Ethiopia and Yemen, but accomplished the passage of the Bab-el-Mandeb "with no confrontation" on the night of 27 September.

Participating in a Gonzo Regatta at the conclusion of that period, competing in both gig and motor whaleboat events, Davis won the former race, with Rear Admiral Bryan W. Compton, Commander, Carrier Group 6, presenting the award to the boat officer.

Over the ensuing months (July–August), the crew learned of "growing evidence to expect de-commissioning in late December..." but the ship deployed on 23 August to participate in United Effort/Northern Wedding-82, "an operation of NATO [North Atlantic Treaty Organization] forces larger than any peacetime exercise before."