"Cheap Tripod" is just another way of saying "First of several tripods". The reason you use a tripod is because you want a rock solid foundation for your camera that won't move. Anything less and you might as well hand hold. For me there are two varieties, big, bulky and solid, and travel. There's no forgiving movement in the former, and for the latter you want something solid that will work in most situations, be light enough and small enough to fit in/on your bag or back, and will allow you to hand something under it to help stabilize it in windy situations.
I know you meant "inexpensive", so we need to know a budget, and a type. Second hand is a good way to go here, and if you've got a decent shop nearby that deals in used equipment it's a great way to save some bucks on what was originally a more expensive piece. I love my Manfrotto 055XPROB tripod with 498RC2 head (just over $300 new). Solid as a rock. I'm also a huge fan of the new MeFOTO travel tripods (I have the Road Trip - $189 new). Thankfully I've found a mounting bracket that will fit on both Arca Swiss and Manfrotto quick releases.
I know it's tough to think about spending a lot on a piece of equipment like that, but realize that if you get something that just doesn't going to do the job all the time then you're eventually going to buy something else, and maybe something else until you either quit in frustration or spend the money you should have spent the first time.