My favourites hotels seems to be pretty booked and expensive that weekend (hotel de russie and st regis) but Eden Hotel is selling at 400 euro per night on expedia that seems a better option for you....

If you are considering Grand Hotel Via Veneto then you can considering several other Hotels always on Via Veneto Area that are selling to a much better prices...

Cavalieri is not any close to the spanish steps...
good luck with your booking