As I have written many times before, I can recommend something to you until I'm blue in the face but you may hate it for your sound. So, instead of giving you a fish, I'm gonna teach you to fish.
Any reverb in existence will get you towards the sound you are looking for--you just may like certain units better. Usability, feature set, tone, it all should play a part in your decision. Surf over to ProGuitarShop and hit their reverb pedal section. Give everything there a listen and pick the one you think sounds the best and has all the bells and whistles (or lack thereof) you want. If you don't like any of those, head to your local guitar shop and play with whatever they have there. Effects require experimentation. I can talk to the utility of certain effects, and even discuss some very nice implementations of those concepts, but in the end it relies totally on the user's taste. That's why there are about 5 billion overdrives on the market. Some electrical engineer out there thought overdrive XYZ didn't do ABC so he made his own to fill out the feature gap.
As for worrying about sounding like surf: surf is a genre that heavily relies on technique in addition to reverb. Whack some 16th notes at around 120-132 bpm with a verb'd out sound plus a slapback delay tone and bingo--you got surf. Play quarters with a dotted eight delay with the exact same reverb setting and you have yourself a nice ambient/textural tone. Effects do not entirely define a genre (as you stated in your question). It's a composite of many, many parameters. See this question for further related discussion on what defines a player's tone.
With all that non-subjective stuff said, here's a list of my favorite reverbs :D. Again, your mileage may vary.
Malekko Chicklet => Tiny, tiny footprint, easy to use controls and a wide range of sounds. It's digital (which is sometimes a no-no for me) but still sounds lush. Were I in the market for a reverb this little guy would be my first stop.
TRex Room Mate => Not for the feint of pocketbook. This one gets you a nice, lush, analog tube driven reverb that is very, very tweakable.
Electro Harmonix Holy Grail => This and it's big brother, the Holy Grail Plus, or the Cathedral are solid choices. All with versatile sounds, and decently affordable. I owned a Holy Grail for much of my early music career and it worked for me.