This is a good question. "somewhere" (just like "everywhere," "nowhere," and "anywhere") is a pronoun, and has the distinctive feature of combining the noun "place" with the relative adverb "where." Your sentence could be expanded to:
- Let's go to some place where we can enjoy ourselves and have fun.
However, when you use "somewhere" the relative "where" is included and therefore not needed:
- Let's go somewhere we can enjoy ourselves and have fun. (when would be wrong, but that would be possible. See the extract from Swan's Practical English Usage below: )
Here is another example I found in the Oxford Learner's Dictionary :
- I know somewhere we can go (= I know some place where we can go).
Notice that in AmE you can also use "someplace" as an adverb equivalent to "somewhere":
- Let's go someplace we can enjoy ourselves and have fun.