Well, on 390 you have some choices. Heading west from old Baylor there is Gay Hill which has a splendid mix of old and new. St. Peter's church--to the south--has two historical markers.
Go to the north, under the single-lane railroad bridge and there are some cool roads. the first goes through the old, commercial, part of Gay Hill--funky if old dilapidated buildings fit your bill.
If you head north, all roads head over to lake Sommerville, and eventually turn left or right. All sorts of interesting places along the way of most of those roads. Take Roads of Texas and a mapping GPS.
West out of Brenham, there are all sorts of quaint things to see in that area heading towards Burton. South of 290 there are some fascinating bits of rang and ag 'stuff' out there--if with varying amounts of road shoulder to stop on.
If you go east on 390, take a left there when it turns right to become La Bahia road. That takes you into William Penn, which has some scenic value.