Of your six criteria, five are feasible ... the conflict arises with the distance factor. You're looking at closer to 40 minutes out, perhaps a bit further. We can come close on taxes, considering that this will not be your primary residence.. Those properties closer in will run considerably more than $200k, especially given the size of the home you seek. Taxes will be significantly higher as well, especially since it will not be your homestead. I can certainly help you if you're willing to drive a bit further. Example: I recently sold a stunning 3200 sq. ft. property, 4br., 3.5ba. in a very desirable subdivision for $189k. Taxes are $4k.
Since this will be a second home, the financing requirements can be a bit more stringent with reference to down payment, interest rate and other factors.
This market is active ... homes are selling almost as fast as they're listed (the one I referenced above was sold within 24 hours). If you'll send me your e-mail address, I can get started with a search, and forward listings of properties that would likely work for you. I look forward to your reply.