
Welcome to the DIS Boards! And congrats on your upcoming wedding.
The construction is the building of the new Disney Vacation Club section of the Grand Floridian. The construction site is located between the wedding pavilion and the GF main pool. Most of the buildings for guest rooms are away from this area and should not pose a problem.
The monorail is reported to have some closed hours during the day. This will vary with their construction schedule. We were there last Fri, Sat and Sun and the monorail was never closed. But if it is, there is still boat transportation to the Magic Kingdom and the usual buses to everywhere else.
Well, the good news is that you should have no problem finding something in your price range, as the Grand Floridian has some of the most expensive rooms on property. Some other lovely resorts to consider are the Polynesian (right next door to the GF) and the Contemporary (also on the monorail line). To get completely away from the construction, consider the Epcot resort area which include the Yacht and Beach Clubs and the Boardwalk. The Boardwalk Inn even has some Garden Suites designed for honeymooners. They are 2 stories and have their own private entrances with a white picket fence! They are adorable!! Plus you a quick walk or boat ride from both Epcot and Hollywood Studios and just a bus ride from the MK and AK. The Crescent Lake area is just totally romantic at night time too.

Something new to consider as you make your plans.
You can ask more specific questions about resorts in the
Resorts section of the boards, as well as discuss al things newlywed related with others planning their special events in the
Disney Weddings and Honeymoons section!
Hope that helps. And have fun planning!

