I'm not familiar with this particular camera, but here is probably the best review you can find:
http://www.dpreview.com/reviews/sonyh7/. Use the menu at the top to navigate the pages.
The last page of the review doesn't seem awfully glowing:
http://www.dpreview.com/reviews/sonyh7/page14.asp. Some things that seem more concerning to me are:
New user interface not conducive to quick operation, convoluted and often confusing
No JPEG quality options (and default setting too highly compressed)
Fairly prevalent chromatic aberration
Strong purple fringing, particularly at wide end of zoom
The bottom of this page here explains the last two:
http://www.dpreview.com/reviews/sonyh7/page5.asp. These two faults are very common among compact cameras, but the Sony seems more susceptible to it.
I'm not so sure about it to be honest.
For a big zoom compact with image stabliser I'd feel better recommending something like:
http://www.dpreview.com/reviews/canons5is/http://www.dpreview.com/reviews/panasonicfz18/I know the Canon's are an excellent camera and they would be my first choice. Although I don't have first hand experience with the Panasonics, I've always heard and read good things about them.
Whichever way you go, I'd consider something with a swivelling screen. That can make a huge difference and I'd kill for one on my SLR. Shooting above your head or down low or at a weird angle is a total walk in the park with a swivel screen and I loved it when I had a camera with one.