I dunno if you already have a camera, aside from the iPhone. But one thing to consider is to get something that has features you don't already have in your iPhone or other cameras.
For example you already mentioned GPS. Although you can tag stuff later, it is a very nice feature to have if you care about showing people where you've been. Not so much an issue if by travel you mean mostly cities, but if you hike, bike or go to more off-track areas it's quite nice.
Wifi capability is also something to consider. I know you're trying to avoid that, but when you do have a phone it can be very fun to operate the camera remotely, download pictures from it, and so on. Can make it easier to share photos with others who have phones; my Olympus, eg, can beam shots right to other's phones via an ad hoc wifi connection.
Zoom. Some compacts have surprisingly good zooms (or even super zooms). Can be very handy when traveling.
Weatherproof compacts are nice if you doing watersports. I have a Panasonic TS5 and love taking photos in tidepools, on river trips, etc. It also has a time lapse mode, wifi, GPS and great video. Other brands in the same category are similarly capable.
Any of these could supplement a smartphone camera and not necessarily duplicate it's functions.
Or just go relatively cheap; there are tons of bargains out there on cameras that would do better pics than a phone for not much money.
