Brenham National Bank is good. There is a minimum to open an account but you don't have to keep a minimum balance.
They don't have a bunch of ATMS (they just have one local bank and the others are in Btrenham and Chappell Hill), but they waive the fee or reimburse you if you use another bank/business's ATM machine. (I don't use ATMs all that much so can't remember exactly how they do it, but it doesn't wind up costing to use them).
Also, if your college student will be stopping by the bank in person any, they might be interested to know that they have a freezer full of Blue Bell ice cream so when you go to the bank, you can get a little cup of ice cream and a wooden spoon or can get an ice cream sandwich or fudge pop. (They don't look at you weird if you decide to grab a few).
They don't charge you for having an account (if there's more than one option, ask for the free checking and they should know which one it is) and they don't charge you if you want to go in. (I can't remember which bank does that, but I know there's at least one that does).
Also, they put deposits in before they take out purchases, and they count a deposit the same day it's made, so it's less likely for someone to mess up and accidentally wind up with fees for insufficient funds.
They are at Southwest Parkway and Highway 6 (across from Allen Honda), so you do need to be able to drive there. I can't remember which banks are walking distance to A&M, but they aren't.
They are very nice and will recognize customers that have been there before; feels more personal than some of the larger banks.
Anyhow, highly recommend; not just because of the ice cream, but it definitely makes a trip to the bank more enjoyable. (They do also have DumDum lollipops at the counter. I'm sure the ice cream is because their main branch is in Brenham, where Blue Bell is from, though).
Edited to fix typo
