As I went through this process a little while back, I can give you a little info on some good 4x4 SUV options to start your search with.
2nd Gen Nissan Xterra: Very good, somewhat compact 4x4 SUV. Engine has got a lot of torque. It has an optional 6 speed. Robust (Body on frame with solid axle in rear and independent front suspension), and mostly reliable (I would stick to 2011's and newer, as supposedly there were auto transmission issues with the earlier ones). Buying new, many dealers are offering these at a big discount (overstock, plus this generation has been out for nearly 10 years). Not uncommon to find some used ones for about $15k-$24k depending on the mileage and trim level.
Downsides for this one would be mediocre to bad mpg and small fuel tank limits your driving range. Top highway mpg is about 20mpg for the 4x4 version (6 speed supposedly gives a slight improvement, but not much). Rear Leaf springs eventually sag and need to be replaced and/or upgraded. Front diff has been known to have issues or break with hard usage (think extreme off-roading where wheels are coming off the ground).
4th 4unners: 4th Gen (prior to 2009) has a torquey v6 or optional v8. Very reliable. Coilover suspension on all four corners (no leaf springs that will eventually sag out). Again robust body on frame construction with solid rear axle and independent front. Good reputation and as a result have good resale values on the used market. Generally used ones (under 75k miles) will go for anything between $14k-$23k.
Downsides: Toyota tax - even though this is very similar to other BOF SUV's like the Nissan Xterra, you will generally pay more for these because of Toyota's reputation (perceived or real). Sits low to the ground, so if you intend to do more serious off-roading, it will require a lift.
5th Gen 4Runner: Updated frame and drivetrain from 4th gen. Similar 4.0L v6 as the 4th gen's but with more HP and better mpg. Solid rear axle with independent front. Comes with higher clearance. Various trims to choose from that offer different options. 22mpg highway and 23 gallon fuel tank means you'll have a max driving range of about 420 miles, which is pretty good for a Body-on-Frame SUV. Generally used ones are going for $23k-$33k depending on the trim and mileage.
Downsides: A bit bigger than both the 4th gen and Xterra (can be good or bad depending on what you're looking for). Engine and drivetrain performance is nothing special, especially for the money you are paying. Nissan Xterra's and 4th Gen 4runners offer nearly the same level of performance at lower prices.
R51 Nissan Pathfinder: Made from 2004-2012. Since its the older generation, you should be able to find some for very good deals (anywhere from $11k to $23k used). Bigger and more room than the Xterra. Optional V8 if you want it.
Downsides: V6 is pretty much same engine as the Xterra's. So same mediocre mpg and small fuel tank limits your driving range. Sits low to ground, and will require lift for off-roading. Unlike the other 3 SUV's, this though its BOF has independent front and rear suspension. Not a huge deal for daily driver use (if anything it will make the drive nicer on pavement and graded surfaces) though in extreme off-roading you might want to swap/upgrade.
Those are pretty much the options for 4x4 Body-on-frame SUV's that are somewhat recent. If you don't care about the body-on-frame aspect and just want 4x4, you can also look at pretty much any of the crossovers Jeep is offering (Grand Cherokee, new Cherokee KL, Renegade, Liberty, Patriot, ect.).
Edit: Changed Pathfinder designation from R52 to R51.