Find an older bike you like with horizontal drops and take off all the gear crap as well as the extra chainrings. Redish the rear wheel. Add spacers, etc, to get the chainline right. Oh forgot, get a screw on freewheel.

Yes you need wrenches to change flats and no QR won't work on rear. If the distance isn't too great look for an old chromoly mountain bike with horizontal drops to convert.

I got a 19" Specialized hardrock chromoly frame/fork with horizontal drops for 41 dollars on Ebay. Police auctions, thrift stores, garage sales, etc. For the newer frames surly, iro, nyc bikes, etc, etc.

Also on ebay i got an old Fuji s-12 which i converted to fixed gear by adding a cheap 700c fixed wheel set and a different crank/chainring/bottom bracket.