Hi M.,
A few things I did when my daughter was that age and I needed to get out of the house:
*Walk around the mall with her in the stroller, early morning before the stores open. Most malls open around 7am for walkers (look for where all the cars are parked to know which entrances are unlocked at that hour). You can breastfeed near the escalators where they have the nice sofas and chairs set up. (Also, once the mall opens, Nordstrom at Chandler Fashion has a nice room in women's restroom.)
*Baby lapsits at the library, which you are already doing
*Moms breastfeeding/support groups through the hospital. Banner Gateway, Banner Baywood, and Gilbert Mercy all have them. It's so nice to be able to talk with moms who have babies of the same age. You do not have to have delivered there to attend.
*Stroll around Babies R Us. They have a nice breastfeeding room.
*La Leche League has a 'Baby and Me Cafe' once or twice a month in Tempe and in the East Valley. They meet at a coffee shop or park and just hang out and chat. Easy to breastfeed there, for sure! You do not have to be a member to go to these. Check out http://www.lllofaz.org/ and click Phoenix Metro area to find the locations for that month.
Good luck!
T.