Just so you know - HWY 87 is being 4-laned and so you'll probably run into some construction. I haven't been up there since June, but it was still going on at that time and looked like they wouldn't be getting finished any time soon. Nothing horrible then, but just wanted you to be aware. It is a beautiful drive once you hit the Island. Part of it is through National Seashore land.
There is one gas station on the Island on the east end, where you'll come in if you take 87 I can't remember how the pumps are oriented. I know there are choices farther north on 87 which have pumps parallel to the building as we've used them in the past. If you take I-110, there is no handy gas on the Island for your RV. As AlabamaTraveler said, top off ahead of time, and I'd suggest you do it before you cross the 3 Mile Bridge into Gulf Breeze. There are 4 gas stations in Gulf Breeze, but at 36 ft none of them would be my first choice for fuel if I were you. The 2 most RV friendly ones are on the east side of Hwy 98, so they're hard to get to when you're heading south. We're a gasser, so if you need diesel you'd need to verify who has it. Not sure if all the stations around here do.
There's a big station on the right soon after you come off I-110 onto Chase Street. You would need to be in the far right lane. You can either exit back to the right out onto Chase Street - getting into the center lane or far left lane - or exit left out the other way (toward the water) and turn left onto Main Street. Both take you to the 3-Mile bridge which is clearly visible from the station so you can't miss which way you need to be going.
Norm is correct, there is some very good food here, both on the Island and in Gulf Breeze. And we are very casual out here on the Island. You're coming to a beautiful place that I'm blessed to call home. I live on the west end, about a mile from the beginning of the National Seashore land. If you have more questions ask away and we'll do our best to help
Safe travels.