We have always enjoyed Planet Fun (PlayIt Fun as my 3 year old says!) It is a lot more affordable than Chuck E Cheese, and has better pizza! We had a bday party there and the kids had a blast. It seems dirty but Harrison would much rather do the physical things there than the games at CEC.
In the north valley there is a great little park called Columbus Park. I don't recall any bathrooms but I have a boy so it isn't much of an issue (just kidding!) The playground equipment is all by Little Tykes and in the theme of Columbus park, it is a big ship, with palm trees around and crocociles to ride/step on, even has like a plank to walk on the ground. It is south of Montano and 4th, back behind Douglas McArthur elementary school.
Also, the Los Ranchos park (Hartnett Park) has great shade and is a very nice and relatively new playground, and has bathrooms. That is at the corner of Rio Grande and Chavez. There are tennis courts there as well.
Corrales Park is nice, with shade and bathrooms in the library except the equipment is not shaded and gets very HOT to the touch!