Well the biggest problem you'll have is that a good portion of the white tanks is now either County Park or now part of the city of Surprise. I assume you will be archery? Rife is not allowed at all, I know that a person used to be able hunt archery within the county park but had to check in at the gaurd station to declare that they would be hunting. I heard a while back that all hunting including archery was eliminated from the white tank park but have not confrimed this myself.. The only place that would be open to hunting that is not either city prop or county park would be the extreme west side of the tanks.. Probably accses this part from the bell rd/sun valley parkway rds.. An associate of mine at work said that he and his family used to hunt the way up on the west side for years, and like most desert regions of AZ there are few deer but there are big ones to be harvested. I've personally only seen a few does but in the park area,, I've done quite a bit of quail hunting on the backside but have personally never seen a buck in there.
I took my nephew to the hunter Ed course out in Buckeye about a year ago,, and on one of the nights we had the wildlife manager for unit 42.. We had a long discussion about impact of motorized vehicles motorcycles, etc on Wildlife.. I remember him using the White Tanks as an example,, specifily the north and northwest portions of white tanks have roughly only 5% of the deer they had only 15 years ago, due to all the off road vehciles, motorcylces,, etc...
I guess I would not try my luck there... If your looking for someplace close by besides the tanks, I can point you in a few directions that you should increase your chances in spotting a buck. Send me a message if your interested..