Cove's is 45 mins. south on their shuttle so most of Nassau's north side is an option - you just have to be near a pickup point.
That includes most of Paradise Island, Cable Beach or downtown.
There's a couple Suites properties on Paradise Island. Comfort Suites has their view partially blocked by the Atlantis towers so guests have "privileges" at Atlantis - IDK what they are, The other property is the Best Western - it might have views of the channel btween Nassau and PI.
I do not recommend the Holiday Inn at Junkanoo Beach, it was old in the 80's. If you aren't renting a car, I wouldn't if Cove's is picking you up, there's shuttles that run between downtown, P.I. and Cable Beach often. There's also a ferry that docks just to the east of the cruise pier/downtown, it goes to Atlantis.
Orange Hill and another B&B used to package deals with Cove's also. IDK OH but the other one was not near much.
The farther east you get past downtown the grungier it gets so don't befooled by some of the small, inexpensive resorts near the harbor, Cove's won't pickup there either.
A few of the smaller resorts bordering the PI Golf Course looked decent but they're not waterfront.
If you aren't diving every day, Atlantis is worth a look, they have Dolphins, Manta Rays in a huge "
"Atlantis" exhibit, standup paddleboarding and the casino/night life.Not the best beach though. Cable Beach can be crowded also, some of the big tower hotels put out hundreds of beach chairs.
Everything is Expensive on Nassau - starting wth the airport cab ride. Food also since it's all imported.