Go with the Lancaster Gate hotel; it's a good central location, close the the tube (Central Line, which is convenient), and to the park.
That hotel is in Bayswater, right in the middle of it. It's a quiet area, not at all hectic.

I have been to both Venice (three different times) and Rome in February. Maybe I was lucky but the weather with expectation of a day or so was lovely.

Hotel prices are better and the crowds are less.

You can visit the whole North of Italy with train and I think that it is an great option to do actually. My advice for you is to skip Milan (even if there is some nice things but in reality it is just a hype name) and instead of it try to visit some other places like Venice, Bologna, Turin, Verona and other smaller towns. All in all Venice is the most in every combination you make so be sure to spend at least one full day there. Pay special attention to prices because it is a touristic place. Here is some short Venice experience that might help you in your trip : http://personal-travel-photos.blogsp...ice-italy.html