There are not really suburbs around Topeka - just other small towns. If you don't want a small town, Lawrence is really fantastic and not too far, about 20 miles to the East. They school district has two high schools (yes, lots of students, quite large) but the grade/middle schools are broken out into smaller schools. If you want a small town, Silver Lake has a good reputation. I grew up in a really small town 30 miles to the NE that I won't recommend (or comment negatively on in a public forum
) Others are good as well, those are the first two that come to mind.
I am not sure what $300K will get you in Lawrence, but I don't see it as a problem to get something nice. Anywhere else, you definitely should find something that makes you happy. Housing in KS is pretty dang cheap still. It still makes me smile remembering my mom complaining about spending $69k for her house in 2003 that she was being ripped off.