There are many D3 schools that are relatively inexpensive, such as SUNY Oneonta in NY or Ramapo in NJ, which are public schools. If you look at D3 schools that are good academically and athletically, however, most are private schools. Either way, don't get turned off by the sticker shock. Typical students at Drew can get $15000-25000 in aid. Very few (less than 5%) pay full tuition here.
Obviously, part of what someone is looking for is a good academic fit. Also, if tennis is important, the ability to contribute to the team will be an important factor. Many coaches are good recruiters, but don't know much about technique or strategy. Just because a team is good, doesn't mean that the players improve. I will give you an example, this year 2 of our players got to rematch 2 guys that they lost to 3 years ago. This year, they both won with ease. In one case, the opponent got worse, while my player improved, and in the other case, my player got signifcantly better, while their's didn't improve. Another thing to consider is the location of the school. Especially if you are coming from a great distance away. Some schools are not near an airport and barely near civilization, which makes for a very different college experience.
Funny thing, one of our European players came to Drew as a freshman to play tennis and his American girlfriend transferred to Drew to go to school with him. They are still together after all of these years.