I lived there back in the 90s so my local knowledge is not current. I can tell you that there are few choices for good public access golf in NW Arkansas. There are some great private clubs there, but to get on, you have to have connections with a member. FWIW, the Razorback golf teams play at Blessings, which is an exclusive private club not far from campus. Pinnacle CC in Rogers is where they play the LPGA Wal-Mart tour event. But it is also private.
Most likely your best bet is going to be Stonebridge Meadows. I have not played it. Might want to check out their website (stonebridgemeadows.com) and decide if you want to give it a try. About the only other option is Prairie Creek up in Rogers. It's ok, nothing great.