Old Forge vs. Indian Lake with kids

I'm planning a trip with my boyfriend and his kids (4,8,9) the first weekend of October. The kids are very fit and may want to hike a mountain (4 year old can be carried at times) . We're considering renting a place and either staying in Old Forge and climbing Bald or Black Bear Mountain, or possibly Indian Lake and hiking Blue or Sawyer Mountain.

Looking for recommendations on location and mountain. Will the weather at the summits be reasonable with jackets? We'd like some fun activities for the kids on a non-climbing day, but it's not required. The kids are easily amused with small country corner stores.

Thanks!