re: Poker & Any sites with HU for play money?
I'm not aware of any play money heads up either but PokerStars
has $2 + .20 heads up tables. It's not quite the $1 that you're looking for but it might be worth considering.
Apart from that, the only thing I can think of is to sit yourself down at an empty play money table and wait for a person to join you. Then you'll get some heads up play until other people join. Then leave that table, and go to an empty table, etc. A bit of a hassle, but if you don't want to spend too much, then this might be an option.