Southwestern in G'town used to be the most expensive school in the state, although they traded the title, off and on, with SMU in Dallas. Don't know what the cost is now days, though.
Anyway, it is an excellent school, very small, and leans toward liberal arts, I think, although they do have a natural sciences school that I know of. I would expect they have something in computer sciences, but very little in the way of engineering. I think they have a 'pre-engineering' program that lets you transfer into one of the engineering schools after two years without being behind. Oddly, they are on the trimester system while most of the state of Tx is on semesters.
My sister graduated from there (many years ago

), and as far as I could tell their philosphy was...if you can pay, you will (through the nose), but if you can't, we will give you the money from the people that could pay.....My sister received several sizable grants that really helped.
You might consider Baylor, it is a larger parochial (sp?) school with more options. It is in Waco (big minus), but G'town is not exactly hopping and at least Baylor has 15,000-20,000 students to hang with instead of 1,500.