You need to make the trek to 183 and hit Pinballz. He probably has a couple hundred machines in there now - amazing collection in great shape. There are a few machines scattered around town here and there, but in many cases, condition will be poor.
From downtown, it is only about 10 minutes to get up to Pinballz by way of Mopac (loop 1) North, assuming you aren't trying to do it at rush hour.
PM me if you want suggestions for Austin restaurants/night life/hotels/etc. Weather is typically really nice in April.