I rode a friend’s DRZ400 for several weeks and used it to pass the Cali DMV test. Really fun bike, especially around town. If I was looking for a town or short commute bike, the DRZ would be at the top of my list. It’s just awesome how you can slip through traffic, create parking in dirt patches that scare off most road bikes and hop off curbs at will. It was fine on short fwy jaunts with no issues at speeds up around 65 (I didn’t try faster, so can’t attest to top speeds).
The KLR is also a great bike, but the fuel tank is huge and adds quite a bit of weight up high. Still, I don’t think you need to worry about either bike being top heavy. You’ll quickly get used to it and you’ve got the height needed to keep them upright (unlike me, who had to basically hop onto the seat to compress the springs enough to get one toe down!)
If I ever get a garage big enough for a second bike, it will probably be a 250-400 dually “town bike”.