I think that as long as you can keep a lot of succulents and cacti where you live, you're going to be able to keep melons, because they need a lot of sunlight. If you like Honeydew, I would recommend
Honey Dew Melon (Cucumis melo var. inodorus 'Green Flesh'). I found it was an easy one to start off with, and if it hadn't been for us starting to move I believe I may have at least gotten two melons (because I saw two flower buds). But unfortunately we started getting involved with moving to SD, and I didn't really have time to tend to my plants.