I'm a local (well, Houston area, so not PSX local...maybe "regional"), so I can offer some info. Not sure where you're coming from, but if you're considering those two locations I'd suggest you consider a third: KLBX Angleton/Lake Jackson, and the
Runway Cafe that's on-field there. (Call and make sure they're still open; I haven't been there in a little while.) You can taxi right up to and park at the restaurant, and if you want to top off, the SS fuel on the field is consistently some of the cheapest in the region. The restaurant is casual and mostly fried seafood, which is reliably tasty if not exciting.
I have not been to PSX in years, though it was my solo cross-country destination during my primary instruction and I landed there several times during my training and shortly afterward. Back then, on-field services and FBO support were...sparse. Looking at the Airnav page, it doesn't look like that's changed any. SS fuel, and no reviews or FBO website listed. Used to be, you could call a nearby restaurant and they'd come pick you up, but I haven't tried that in a long time and don't know if they still do that, or if the restaurant's even still around...I can't remember its name. Looking at Google Maps, I think it was where
Danny's Seafood House is now, though I don't think that's what it was called when I went there.
KGLS is an okay choice, but unless things have changed there's no crew car available. Taxis/Ubers are, though. You can also walk a short distance to
Moody Gardens, which has a steakhouse (only open for dinner and requires reservations) and a more casual sit-down option (walk-in for lunch or dinner is no problem). Just don't expect to be blown away by the casual option. It's got a different name than the last time I ate there so maybe it's better now, but historically it's been very mediocre. An Uber can take you anywhere in town, and there are plenty of good places to pick from using your favorite "find-me-food" app (Yelp, Tripadvisor, etc., or just Google "best restaurants in Galveston"). I usually avoid the Boardwalk area (overpriced and crowded) and Gaido's is kind of "your dad's seafood restaurant" but still very popular, so if that's your thing go for it, but I'd probably pick Casey's next door over Gaido's, and really I'd pick somewhere else on the island besides either. If you're really hankering to eat on the Seawall, I'd go to
Miller's or
The Spot, but I'd personally choose somewhere like
Little Daddy's Gumbo Bar,
Mosquito Cafe, or
Shrimp'n'Stuff (in decreasing order of "fancy" / price), or at least a half-dozen other places more off the beaten track.