Capri's and sandals are good anywhere, so no worries there. I also often travel and dine alone on the islands and have very few restaurants that make feel out of place. But I admit, some are more comfortable than others.
On Sanibel, Island Cow - avg food but lot's of choices and popular with familities - and Doc Ford's (reayy good) - try the mojitos as your drink. Timber's and Sanibel Grill as well. Timber's has it's own fish market, so I really like their fresh fish. The clientel tends to be older and the Grill next door is more lively. (Same ownership) Sanibel Cafe is open for dinner, but I only use it for breakfast and lunch. Cheeburger Cheeburger is good for an easy cheeseburger and onion rings. The grouper ceaser salad at the Lazy Flamingo, a bar - restaurant much loved by locals, is good.
On Captiva RC Otter's, Key Lime Bistro and at the Mucky Duck - get take out bar service and eat outside on one of the picnic tables and listen to the music. With South Seas still closed the restaurants are a little less busy than usual. Bluefish Redfish is getting great reviews for their fish and is so new that you may want to give it a try by dining at the bar.
I'd call the Mad Hatter romantic, but it's so small, dining alone isn't a big deal off season. In season, I might not go. The same for Ellington's, Thistle Lodge, Sanibel Steakhouse, and maybe Portofino's. Other's I'd avoid because I don't think they're worth it are Hungry Heron (yuck!), Morgan's Forest (awful smell), Windows on the Water and Noopie's - over priced and over rated IMHO - and maybe the Bubble Room because I haven't always recieved good service at dinner there when alone.
Hope you have a great trip!