This is one of those questions that is difficult to answer, because each person has his or her personal preferences when it comes to location. For example, I'm a very light sleeper, so any hotel can be a problem for me, so I usually like to rent a cottage near the beach.
What do you like to do? It's still cold, so I'm not sure you'll want to spend time on the beach. If you were flying from Minnesota, it would be different, but it's no warmer here than the East Coast. When I lived in NH and vacationed on Captiva in March, I went swimming in the Gulf, but now I can't get in the water until June!
If it were up to me and I just wanted to "get away from it all," I would drive a little further and stay on Sanibel Island, although I haven't been there for a while. Just a suggestion. The Holiday Inn is the best of both worlds. It's right on the beach, but it also has all the amenities someone spending a weekend would need.
Sanibel Hotel Accommodations with Holiday Inn
If you don't want to cross the bridge, there is a resort in Fort Myers that overlooks San Carlos Bay. Then, if you want to spend a day on Sanibel or Captiva islands, you are only a hop away from the drawbridge.
Dining - Sanibel Harbour Princess Cruises | Sanibel Harbour Resort and Spa
Again, it depends on the type of accommodations you prefer. The above hotel is very nice and has a beautiful pool.
I also agree with Big Munch about Lover's Key, but I don't like the beach as much as Barefoot Beach which is only down the road a mile.
I find the resorts in Naples to be overpriced, but I haven't stayed in one for a long time (since I live in Bonita Springs) When I vacationed here from MA or NH, I was mainly interested in the weather & the beaches. I learned quickly that Aruba was the only place where it doesn't get cold or rain.
Naples Beach & Golf (see link in post by RMD3819) is a very old resort, but it's on a decent beach in a convenient area, very close to downtown Naples. Marco is nice, but not as quaint as Sanibel or Captiva, which is really like taking a vacation away from the hustle & bustle. The Marriott is a nice hotel and is convenient to everything. Actually, Marco is so small that any place you stay will be close to restaurants and shopping.