Which one of the following is grammatically correct?
a) There is a theater, a cafe, and a shop near the park center.
b) There are a theater, a cafe, and a shop near the park center.
Which one of the following is grammatically correct?
a) There is a theater, a cafe, and a shop near the park center.
b) There are a theater, a cafe, and a shop near the park center.
This is a rule of thumb:
When talking about one thing only, then you have to use "there is".
When taling about uncountable things (mass noun) such as water, money, sky etc. normally is used to refer them as a singular. (there is water` there is money etc.)
For more detiles - read here:
Since your sentence detailes many things, then the correct option is:
There are: a theater, a cafe, and a shop near the park center.
The first one.
It's like repeating there is on every comma.
There is a theater, there is a cafe, and there is a shop near the park centre.
If you want to use are, you need the plural for each noun.
There are theaters, cafes, and shops near the park centre.