I'm not a huge fan of FPS games either, but there are some open-world (well, open enough, at least) FPSs out there. Borderlands is the first to come to mind (it has a...very particular style), it's hilarious and it's got nice RPG elements, so it has a decent gameplay depth; however, if you're a fan of exploration you must try out Metroid Prime (the first one is on Gamecube, so you could easily emulate it with a good rig). The atmosphere is top notch even if you're not a sci-fi fan (well, I am, so I may be a bit biased), the gameplay itself is amazing and is focused on weapon upgrades (which are not mere powered up versions of the same weapon), it's constantly evolving.
I'm just gonna skip over all those survival FPSs, because, well...they might technically classify, but I find their lack of character boring. Borderlands and Metroid Prime are both games you're going to remember.