Your combination of requirements is a tough one. You essentially want all of the following in a tripod kit (legs and ball head):
- Compact when folded;
- Reasonably tall when extended;
- Sturdy enough to bother with; and
If you wanted to pick any two from that list, your options are wide open. Getting all five together is a lot more difficult. As usual, I'm going to recommend going to the B & H Photo and Video website and using their excellent search filter to narrow down the choices. This link will get you a list of tripods with heads for under $250 (the filter doesn't have a lower top price to select) that will fold down to between 15 and 20 inches (38-51cm).
I will personally vouch for both the Benro TravelAngel series and the Cullmann Magic tripod. I know they're at the top end of your range in terms of price, but they're certainly sturdy enough unless you're using a very heavy camera/lens combo, they fold down to a very compact and baggable package, are light enough to carry all of the time without feeling like you're being punished for something, and while they're not something a very tall person would want to use all day, every day, they do get tall enough to be useful.
Undoubtedly, there are equally good choices to be had from other makers. The higher-end Velbons, for instance, are worth it, as are the Vanguards. Induro is also reasonably good, but they don't have a model that is as compact and as inexpensive as you want at the same time (you can have either, but not both). I've never laid a hand on the Oben tripods, but they look okay on paper—perhaps somebody else can offer their experience with them?
Unless you are buying used or really on sale, though, I'd try to stick to the upper end of your price range. That $50 really makes a difference in the level of performance, and the next significant step up is another $100 or so on top of that. At the sub-$100 level, you're mostly looking at specialty equipment (like the Gorillapod and its kin) or spindly toys that sort of look like tripods.