Flight
Newark is the closest, best option, but Philadelphia, JFK, and Laguardia are also options. You can either uber, rent a car, or take a train from EWR to the Red Bank (or Spring Lake) train station.
Hotel
This hotel is in the cute town of Red Bank, is on the river, with a pool, about 30 mins from the wedding and 15 mins from the beach day festivities. It's a great spot. If you aren't planning on an extended weekend and/or you don't need to be on the beach, this is probably your spot. If this becomes sold out, the Oyster Point Hotel is next door.
Hotel
If you choose to stay in Spring Lake (which you would do because it's a beautiful, pristine beach town), this is your best bet. Right across the street from the beach, has a pool, etc. The primary downside is that there is a 3-night minimum. Spring Lake is about 15 mins from the wedding and a 30-35 mins drive from the beach day in Sea Bright. So, that too might be a consideration.
Hotel
This is our second favorite place in Spring Lake, following the Breakers Hotel. It's just a few blocks from the beach and has a pool. The advantage of this hotel over the Breakers is that the minimum stay is 2 nights. Spring Lake is about 15 mins from the wedding and a 30-35 mins drive from the beach day in Sea Bright. So, that too might be a consideration.
Hotel
This is a new, hip, modern hotel in a revitalized Asbury Park. Boardwalk and beach right nearby. Asbury Park is equidistant from the wedding and the beach day.
Hotel
Cute B&B by the beach in Spring Lake. There are other B&Bs/Inns in Spring Lake including the Grand Victorian (right next to the Breakers on the beach) and the Spring Lake Inn, a few blocks from the beach. Spring Lake is about 15 mins from the wedding and a 30-35 mins drive from the beach day in Sea Bright. So, that too might be a consideration.
House Or Rental
Most house rentals on the Jersey Shore require 7-day minimums during the summer. So, unless you are coming in the Saturday before (and will stay somewhere else on Sat night, 8/3), this might be tough. But if you want to do a week on the shore, DO IT.
Train
NJ Transit is available from Penn Station, NY and the Newark Airport, among other places. There are train station stops in Red Bank, Spring Lake, other.