The public transit options could be time consuming https://goo.gl/maps/czsNGUSn7rF2
It's only a little over 7 miles, so you might ask your host for the number of a local car service and comparison price that with the train/bus fares.
And are there any other beaches close to Wantagh or in Wantagh at all, easily accessible by public transit or by foot?
The bus to the beach leaves Freeport train station. That is a few towns west of wantagh. You could take the Long Island railroad to Freeport then the bus down to the beach.
I grew up in Wantagh (now live in NYC) and went to the beach everyday in the Summer - and sometimes in the winter. Shoney is correct the only bus would be from Freeport but if you can drive then I suggest renting a car and driving down to the beach - this is NOT walkable. If you do drive to the beach I would suggest leaving your home no later than 8:30am because the traffic down to the ocean is insane. Growing up we would depart home at 8:30am and leave the beach by 3pm to avoid all the traffic. Also as kids without a ride down in a car we would sometimes ride our bikes down to the beach, it's a long ride from the beginning of the bike path (about 14 miles) but as a kid without a car we would do it even though bringing our beach gear on a bike was awful - yet again we were kids without any other option so we did it. If you are interested the bike path it starts at Cedar Creek Park and ends at Jones Beach. mapmyride.com/us/bellmore-ny/cedar-creek-par…
All of Long Island was designed for driving so being without a car is going to keep you very isolated. If you want walking distance to a beach I would suggest staying in Long Beach http://www.longbeachny.gov/Edited: 11:22 am, August 08, 2016
So could you maybe suggest me any other Long Island town with reasonable prices for rooms and beaches I can easily reach?
There really aren't any. Jones Beach is a barrier island that is just south of Long Island. There are no communities on the island where the beach is. There is a boardwalk with concessions and bathrooms.
Staying in Wantagh is about as close as you are going to get, but you will have to use public transportation, as mentioned above, to get there. The bus from Freeport train station is very popular. You might want to look for something in Freeport, but there is not much.
Long Beach is one area that is easily accessible, but there is really only one hotel on the beach and it is not inexpensive.
Our beaches are not tourist areas--they are large and beautiful and popular, but mostly people who live here visit them.
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