This is a mass transit friendly wedding! You can get both to and around Asbury Park without a car. Asbury is a very walkable beach town (it’s only 1.4 square miles) with its own stop on New Jersey Transit (the regional commuter rail system). NJ Transit goes to New York Penn Station, Newark Penn Station (which has a connection to Newark Liberty International Airport [EWR]), and connects to Amtrak’s Northeast Regional (which has stops in Springfield, Hartford, and Boston, among many others on a route that goes from Massachusetts to DC) at Newark Penn Station.
You can drink on both NJ Transit AND Amtrak (although only the latter sells alcohol on board), unless it is St. Patrick’s Day or Santacon weekend. If you're taking a plane to a train, consider economical mini bottles.
The drive is between three and four hours from my parents' house in CT (depending on traffic), and it's a little over an hour from our apartment in Brooklyn.
Free street parking isn't impossible, but can be a little tough even in the off season if there are local events going on, so double check with whatever hotel/Airbnb you book to see if parking is included. There is paid parking near the venue (the ceremony and reception are in the same location) and you can either pay with cash or card at a meter OR use the Asbury Park app (which lets you add money without having to physically go to the meter). The off-season day rate for paid parking is $15.
We’d still recommend that you leave your car wherever you’re staying and either walk or take a Lyft to the venue. If you don’t have a rideshare app on your phone you can call Surf Taxi at 732-774-5500 (their website says they accept credit cards).
I tend to prefer the train to the bus, but you can use either to get to Asbury Park. All train journeys to Asbury Park will put you on NJ Transit at some point- if you're coming from outside of NYC you might also need to do some Amtrak. NJ Transit has the affordability of a commuter rail system (about $30 round trip from New York), whereas Amtrak tends to be pricier because we don’t properly subsidize rail in this country (Hartford to Newark is around $80-100 round trip).
If you live in the NYC area and don’t own a car, taking a bus or train is probably cheaper unless you get a good deal on the car rental and you’re splitting it between four people. The drive is about an hour and a half from Brooklyn, the NJ Transit train ride is about two hours from Penn, and the Academy bus ride is allegedly an hour and a half from Port Authority.
From New York Penn Station, get on the NJ Transit “NJ Coastline” train towards Long Branch and get off at Long Branch. Transfer to the train heading towards Bayhead and get off at the Asbury Park stop. NJ Transit has an app you can download to plan your trip and to buy tickets digitally, but it's kind of a messy app in that if you check it too far in advance it makes it seem like there are no options, so just be aware of that! You can take a dog on NJ Transit for free if it’s small.
From Port Authority, you can take the Academy Shore Points bus, which makes three different stops in Asbury Park. It's allegedly a 1 1/2 hour ride but with traffic it might come out even with the train, so I'd mostly consider taking the bus as a backup if the train doesn't work for some reason.
Take the Amtrak Northeast Regional train to either New York Penn Station OR Newark Penn Station. At either station, get on the NJ Transit “NJ Coastline” train towards Long Branch and get off at Long Branch. Transfer to the train heading towards Bayhead and get off at the Asbury Park stop. The ride from New York Penn Station is about two hours. NJ Transit has an app you can download to plan your trip and to buy tickets digitally (and so does Amtrak), but it's kind of a messy app in that if you check it too far in advance it makes it seem like there are no options, so just be aware of that! You can take a dog on Amtrak if you pay a $25 fee (and if you book early enough), and you can take a dog on NJ Transit for free if it’s small.
As a purely academic exercise, if you dislike trains, you could take some kind of Greyhound or Megabus to NYC (Port Authority), then hop on the Academy Shore Points bus. I probably wouldn't go this route because the snack options at New York Penn Station are better than the ones at Port Authority and trains are generally more comfortable, but you could technically do it.
NEWARK...Laguardia...Kennedy [Davenport]
...are your airport options, but Newark is the nicest airport of the three and is much closer. From there, it's probably easiest and quickest to take a Lyft (I've checked it a few times at different times of day, and it's ranging from $65 [non-rush hour] to $100 [weekday rush hour] without a significant price difference between shared or single) or rent a car and drive to Asbury from the airport (45 minutes).
If you're in the larger Flanagan family and you're flying in, your best bet might be to take a Lyft from the airport and seeing if one of our relatives can drop you off at Newark on their return back to Massachusetts (it's on the way), since you won't need a car while you're in Asbury.
BUT we love a transit challenge in this household, so let it be known that you can also take public transit from the airport by doing the following:
This should theoretically take around two hours. There's also a bus-based route you could take- you can look up both the possible train and bus routes in the NJ Transit app. (Note that the NJ Transit schedule changes seasonally, so the app will sometimes not show that trains are available if you put in a date too far in the future.)
Financially, this would be an absolutely ridiculous route to take. But in the interest of plotting all possible Escape from New York routes for any Snakes Plissken out there:
Take the Seastreak Ferry to the Highlands stop (the last stop), which takes between 40-60 minutes from Wall St. This costs $47 round trip which is more than the train or bus. Then, take a half hour Lyft ride to Asbury Park.
BONUS: Take the NYC Ferry ($2.75) to get to either Wall St or 35th St for a multi-boat journey featuring Pocky and alcohol. You can take the ferry from Brooklyn (Greenpoint, Williamsburg, Brooklyn Navy Yard, Dumbo, Red Hook, Sunset Park, Bay Ridge) Queens (Long Island City, Astoria, the Rockaways), Manhattan (much of the east side + Roosevelt Island + Governors Island) or the Bronx (Clason Point).