Can't think of anywhere better for you than Calis. Its very friendly and relaxed and everything you need is in easy walking distance. Fethiye is good for shopping or for a walk around the harbour, you can take a nice trip over on the water taxi, but personally wouldn't want to stay there myself. Agree that the Mutlu would be a good choice, it's a good hotel and right on the promenade. The Oykun is also a good hotel, we've been there twice ourselves. It's further away than the Mutlu (about 10 mins walk to the promenade) but since the road outside has been paved over this year it's much easier walking. They are also very well set up for people with walking difficulties. There are no lifts but all around the ground floor wherever there are stairs there are also ramps to make it easier. The staff there are wonderful, and if you request a ground floor room I know they will do their best to accommodate you. There are often women travelling on their own staying there and don't seem to have any problems mixing with other guests and making friends.
I'm sure you'll love Calis if you decide to stay there. And be back!