The game I played right after GF was The Dig, also by LucasArts. It's different but easily my second favourite LA game after GF.
You may also like Beneath a Steel Sky. Some bits of it remind me a little of GF. It's freeware nowadays so you aren't going to lose anything but time if you don't like it.
Also, if you manage to get your hands on the Gabriel Knight games, give them a try. GK is by far my favourite game series ever. They offer a well researched backstory, great humour and suspense.