Mondays at RTC, can't remember if it's at 10 or 10:30, Mr. Knick Knack performs at the pavilion (where the ice rink is during the winter). My DS really enjoyed it over the summer.
Did you check Reston Library? The library newar me has tons of kids/baby programs. Like pp said, Mr Knick Knack sings on Mondays at 10:30 through Oct. She could check meetup.com for other groups to try. The YMCA might have something too.
Not exactly Reston, but not too far-Jammin Java in Vienna has kids performances everyday at 10:30. It's a different performer each day and $5 per adult.
Re: What to do with a 10 month old in Reston area
Clemyjontri Park in McLean isn't too far and it's awesome. There is also Frying Pan Park.
I also stumbled on this blog the other day. Not updated often, but still lots of ideas:
https://restonwithkids.blogspot.com/
Not exactly Reston, but not too far-Jammin Java in Vienna has kids performances everyday at 10:30. It's a different performer each day and $5 per adult.