I go to Gib' a lot with work. It's a small place so I'd not plan to spend much more than a day or two at the most there. It is a peculiar place, a very British enclave off the south of a somewhat industrialized / run down bit of Spain. I imagine if you've never been it'll be at least a novelty but I struggle with that having been over so many times for work, it's just become a site that's a right PITA to fly to

I'm back out next week and then again in two more week's time (First World problems, eh

).
If you like tapas there's some good places in La Linea (the town just over border in Spain, you can walk over from Gib' with a passport for the night). Particular favourites are Patagonica (there's also one in Gib but the original Spanish one is my favourite). The tapas is worth hunting out from there, the next one is even better and completely Spanish. If you like steak (huge ones) go to Gauchos but it's expensive, the nicest I've had has been one in a place call Paparrazi, a little off Main Street, both in Gib.
Casemates Square and the bars / restaurants there are tourist traps IMO and pretty variable quality. Great wee curry spot down near Queensway Quay (Raj's Curry House), tiny, a bit rough round the edges and curries are a little different to the usual fare but still good.
Walk the Mediterranean steps, up Eastside if you're there, along the top (heading north) and then down either the cable car (most vaguely exciting location, most disappointing cafe, other than the ones in the airport terminal) or just down by the Moorish Castle. Don't waste your time or money on the taxis, IMO.
St Michael's Cave also OK but better to pre-arrange a tour into the deeper ones, apparently much more impressive. I haven't the inclination to do it myself as spend a lot of time in the tunnels / tanks. Caving when not working doesn't appeal ;-)
Europa Point is OK for a lounge, ice cream and to see Africa from Europe.
Agree with others that Rhonda and Tarifa are both very nice.
Any other questions or info needed drop me a line / PM. As I said, bit jaded about the place as it's a drag going out there so much so take my comments with a pinch of salt / some caution.