>>11952211PhD here. Honestly, as long as you stay in undergrad, no one gives a shit where you went, as long as it wasn't some sketchy backwater school below 2000 in rank. Likewise, GPA really doesnt mater out of your first job either.
To the working world, a degree is a degree, and as long as its not something like MIT, they wont care where you went.
This changes a bit in grad school though. Where you graduate with a masters isnt too important but your PhD should be at a top 100 school in that field. Not "do or die" by any mean, you can get by with a degree from the best in your state or some nice little college but it helps. After your first few research papers, where you graduated becomes irrelevant, much like how your school/gpa becomes irrelevant after your first job.
I had a terrible undergrad GPA but since my GRE was so good and I had the backing of a professor, I was able to get into grad school. Did great in it and got through with a 3.92, went out and started working at a research center, and now no one really cares about the little school I went to, they only care about my publications and just see the "PhD", not the school.
So to answer your question, as long as that school is a nice fit for you and is indeed a relatively known one, you should be fine. Its better to go to a smaller, more intimate school where you can actually learn and do stuff than one that just pumps out graduates without a care in the world (Looking at you UT)