Question

There is not the subject, so use are.

Compare these:

There are a swimming pooI and a park near my house. (There are two things near my house.)
There is a park near my house. (There is one thing near my house.)
There is a swimming pooI in the park near my house.

There are a swimming pool and a park.I think so.)

AnonymousThere are swimming pooI and park.There is a swimming pooI and a park.

The "there" construction ends with a phrase of location. Your sentences lack that. You need something like this:

There are a swimming pool and a park in that area of the city.
There is a swimming pool and a park in that area of the city.

In the "

CalifJimIn the "there" construction with a compound subject, if the first subject is singular, both the singular and the plural verb are acceptable.

This I did not know.

I have to say that my ear does not like the sound of "There are a swimming pool and a park..."

Aspara GusThis I did not know.

I found it on a couple of grammar sites years ago. It stuck in my brain.

Michael Swan, In his Practical English Usage (2005.525) says:

In an informal style, here's, there's and where's are common with plural nouns.

Here's your keys. .......There's some children at the door........Where's those books I lent you.

fivejedjonHere's your keys. .......There's some children at the door........Where's those books I lent you.

Not to my ears!

Here're your keys. etc.