Can I bring my 9 and 10 year old children with and have them sit at a table for an hour while I work out?

I would call them first just to make sure.

That shouldn't be a problem. I would give them a call first

I would call the location. Some locations have a good seating area but most are tiny, one or two tables right in the front of the work out area. They use it for classes, new members and people to wait for tanning/massage. I am also unsure of the children policy, I'd call your location.