Kevin Rooney said:
Another vote for Kearsearge North. The views begin fairly early, and there's an enclosed fire tower that's easy to access on the top.
Agreed - Kearsage North is 6.2 miles round trip and a solid 2,500+ vertical (more challenging in my opinion than some of the easiest NH4Ks, but the views are awesome).
Black Cap is probably the easiest peak with a view to hike to (Great Hill in Tamworth, about 20 minutes south, is easier and has a fire tower) in the area (about 700 vertical, 2.6 miles RT from Hurricane Mt. Road). It can also be combined with Cranmore.
Also, White Horse Ledge and Cathedral Ledge are both nice hikes (and can easily be combined if you hike up the Bryce Path) just northwest of town (about 900 vertical for White Horse, probably another 300-400 if you add Cathedral).
Middle and Peaked Mountain can be done together - nice shorter hikes with decent summit ledge views (about 1,300 vertical for Middle alone, add another 500 for Peaked with it).
South Moat is another nice hike (there's a new trailhead/parking lot a bit further down the road then described in a lot of guides/sites). Alone, its about 5.4 miles RT, circa 2,200' vertical one way. Middle Moat can be added for another 200' vertical one way - mostly above treeline walking on the top of that ridge.
Iron Mountain is just about north of North Conway (closer to Jackson) and is a fairly tame hike - about 800 vertical. There's nothing to see on the summit (except for rocks and ruins of an old fire tower), but there are a few nice lookouts just below it. Unless the birds/bears/hikers have beat you to the punch, there should be a bunch of ripe wild low bush blueberries along the way.
Pleasant Mountain in Maine is less than half an hour from North Conway and has nice views via multiple trails to the summit (circa 1,500 vertical, 5 or so miles RT).