Old Wives Tales (restaurant) - has a great kids area, is economical, and is good with dietary restrictions. Plus they are on the east side somewhat near the Lloyd Center area.
Barnes & Noble at Lloyd Center has a storytime - check their web site for the exact time / day.
The pirate store at the mall also has story times occasionally.
Matt Dishman Community Center just a bit north of the convention center area has a pool and perhaps a toddler indoor play park during the summer. Depending on your preference and the use of a stroller, they may be within walking distance of your hotel.
On the same street as MDCC is the"Title Wave" Used book store. It is old library books that are for sale.Very low key, friendly folks, even if you just wanted to hang out and browse.
Yes, the fountain at the Rose Quarter. Also Jamison Square in the "Pearl" -just across the river on the west side.
Pioneer Square in downtown Portland frequently has something free going on - check their web site.
The central library downtown is also great -lots of books (of course!), story times, free shows, concerts, etc.
Enjoy this great city!!