There are a couple of ways you can rephrase the example that might make it easier to understand. All of these are grammatically correct:
- Watching sports is a very social pastime and best experienced at the place where the match is unfolding.
- Watching sports is a very social pastime that is best experienced at the place where the match is unfolding.
- Watching soccer is best experienced at the stadium.
- Watching soccer is best at the stadium.
- Hockey is best watched at home.
- Chess is best played with friends.
- I play soccer poorly, basketball well, and hockey best.
In each of these cases, "best" is modifying (acting on) the closest verb.
In your example "experienced" is the verb that is receiving best. It may be confusing because sometimes, "experienced" is also used as an adjective (meaning expert) (link).
He is a very experienced carpenter.
Here, it is a verb in the past tense:
I experience, I am experiencing, I have experienced it, I have experienced it best.