When it comes to small CUVs in the U.S., the most popular (in order) are:
Ford Escape
Honda CR-V
Chevrolet Equinox
Toyota RAV-4

With that being the case, you really can't go wrong with any of them. They're mechanically pretty similar; basically a tall FWD car with a clutch-based AWD system. They get pretty good fuel economy, but the tradeoff is generally poor off-road performance.

If you want better off-road performance, then there are other popular choices:
Jeep Wrangler
Jeep Liberty
Nissan Xterra
Toyota FJ

Unfortunately, the downside with these vehicles is significantly worse fuel economy.

Also worth on honorable mention is the Subaru Forester. On the upside, it offers a better AWD system than what is available in the Escape/CR-V/etc (though not as good as the other 4 listed above). On the downside, if you don't get the 5-spd stick you're stuck with an antiquated 4-spd automatic. The interior is also slightly outdated vs. most of the competitors.

As you mentioned, another one worth considering is the Hyundai Tucson. Hyundai has really stepped up their game in recent years and is offering some real competitive models at very reasonable prices. While I don't think they're 100% there yet in some areas, they are definitely worth looking at. One interesting feature that Hyundai cuvs have is the ability to lock the AWD system into a permanent 50/50 torque split. This can be helpful off-road, though isn't designed for more than casual off-road use.

All in all, I would definitely give them all a look/test drive. More than likely you'll find one you like more than the others based on your needs and price range.

On a side note, I only made mention of smaller CUVs/SUVs, since that's what you seem to be leaning towards. If you're having any thoughts toward mid-size SUVs/CUVs I can also offer some recommendations there.