Yep, eggplant, peppers and basil will go through the summer ok, if you can keep them healthy and clean. There are some interesting tropical veggies like Calabaza squash (that's not really a squash, I think) and Chayote that you can try. Also a wonderful "winged bean" that had square pods and beautiful blue flowers that I had seeds for, and have now lost. I'm going to look for that one again.
But tomatoes? Those are for fall, winter and spring here.
See if you can get a copy of that book, though. The library probably has it, and it has a wealth of info. Once you read it, you'll want to buy it, I warn you. I've used mine so much for years it's terribly worn and dog-eared.