peaks near Concord
38 minutes: Pawtuckaway is a fun set of peaks - it's the rim of an ancient caldera. There's also a field of giant boulders (look for the Boulder Trail northwest of Round Pond)
trail map (on page 2). It's still summer season, so you might want to make a parking reservation . (First, study the map and choose your trailhead. The main parking by the lake is about a mile walk from the hills, so you might prefer the Reservation Rd entrance.)
NH State Parks - Pawtuckaway State Park
32 minutes: Kearsarge (a.k.a. Kearsarge South) is also a nice little peak.
NH State Parks - Rollins State Park
1 hour: Mt Cardigan is another small gem. (Try the Holt Trail if you like very steep trails, but you'll want to go during the week because parking on the east side is insane on weekends.)
NH State Parks - Cardigan Mountain State Park
Mt Monadnock isn't much further - another classic bare peak with fantastic views (but may be very crowded).
But the Whites are actually closer than that. For something quick with a view, try the Rattlesnakes on Squam Lake, or the other Rattlesnake (above Rumney), or maybe Mt Pemigewasset in Franconia Notch, or the Welch-Dickey loop on the way to Waterville Valley, or ....