What kind of sentence is:

The state park in the rocky mountains is beautiful, lots of things to do.

Looking at it as a incomplete sentence but it has an indenpendent clause, the "lots of things to do" is what confuses me.

The independent clause is not the problem. It's the ending phrases that are not properly connected. Try adding "with" or another connecting word.

That would correct the sentence but how would you describe this sentence as is?

It's a simple sentence (one independent clause) with a dangling phrase.

The sentence "The state park in the rocky mountains is beautiful, lots of things to do" is an example of a run-on sentence.

A run-on sentence is a sentence that consists of two or more independent clauses that are improperly joined together without appropriate punctuation. In this case, the lack of proper punctuation, such as a period or a conjunction, causes the two independent clauses ("The state park in the rocky mountains is beautiful" and "lots of things to do") to run together without clear separation.

To correct this run-on sentence, there are a few possible ways:
1. Separate the two independent clauses into two separate sentences:
Example: "The state park in the rocky mountains is beautiful. There are lots of things to do."

2. Use a coordinating conjunction to join the two independent clauses:
Example: "The state park in the rocky mountains is beautiful, and there are lots of things to do."

3. Place a semicolon (;) between the two independent clauses to show their close relationship:
Example: "The state park in the rocky mountains is beautiful; there are lots of things to do."

Remember, it is important to use proper punctuation to clearly separate independent clauses and make the meaning of your sentences clear and concise.