Not to be flip or anything.. but there is no such things as a Hotel on the beach in Miami that is budget friendly. If you do find one that advertises a cheap rate... stay clear as something is not going to be good.
Holiday Inn Port of Miami is a good choice they are across the street from the Port entrance and from the Miami "Bayside" shopping/restaurant area. They are going to run you about $150 for a night (at least the last time I checked that was the price, your mileage may vary) There are plenty of hotels in Miami, but if you are wanting "on the beach" be prepared to spend some cash to do it... OR stay a long way from the port. Last time we were there we just stayed near the airport at a hotel with a free airport shuttle and then taxied to the port the next day so we only had to pay for one taxi ride.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007