General rule of thumb - Hotwire is a little more expensive than Priceline - maybe 10%, but lots of variation. The advantage to Hotwire is that looking at the hotel amenities will often allow one to figure out just which hotel is being offered.
Note the weasel word in the last sentence - "often". The guesses offered by betterbidding are pretty accurate, but no guarantees. I speak from experience here.
You didn't mention time of year? That can make a huge difference in rates.
If you do any Priceline/Hotwire, the Entertainment book has codes for discounts. I just managed to bid 5 nights in Paris at $92@ using the $10 coupon in Priceline (my bid with that coupon was treated as a $102 bid). I have to admit the hotel is out a ways - La Defense area, but looks to be really nice.
Check the Hotel area here on Flyertalk too. You never know just what bargains someone might post.
And I think I'd simplify the itinerary a bit. Much more romantic to sit in a coffee shop somewhere and watch the world go by, than run for the next train, IMO.
Romelle