If the 9-10 year olds are normal, active kids, they should have no problem with hikes of 2 miles or so. I'd worry more about the adults if they are not reasonably active. To view the lakes, you're pretty much limited to the Belknaps, Ossipees, and the Squam range. I second the suggestion to do Mt Roberts, at the north end of the Ossipees. The trail starts at the top of Ossipee Park Road off rte 171 (not to be confused with Ossipee Mountain Rd off rte 109). It's 2.5 miles to the top, and the much of the first mile isn't all that bad. Maybe 2/3 the way up, you are on open ledges, where the views of Winnipesaukee and Squam are. At the very top, the views are to the north, of the Paugus range and beyond into the White Mountains.
Another nice hike, although without a lake view, is Mt Israel, via the Wentworth trail (2.0 miles), with great views north into the Whites. Both Roberts and Wentworth are on the "52 With a View" list started and recently tweaked by the Over The Hill Hikers group. Easily found via Google.
A bit further away, up at the bottom of Franconia Notch, is Mt Pemigewasset (also on the 52WAV), 1.6 miles each way, with an elevation gain of 1253 ft.
For any of these, go prepared for rough hiking. That means good footwear (no flip flops), adequate water (figure a quart per five miles for an adult in summer), first aid kit, etc.
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