M.K.
Hi M.,
I work in Arlington and pretty much anywhere you go you will have walking access to a park! I live in Woburn so I can't help you with the local doctors etc but if you would like, I could hook you up with a rental agent (I work in a real estate office!) to help you find the house you are looking for. You also might want to check craigslist.org for rental listings, just put Arlington in your search.
Good luck with the move and welcome to the 'hood!
M.