Question

1. I am looking forward to my next visit there.

2. I am expecting my next visit there.
3. I am anticipating my next visit there.

(Are they all the same and grammatical? What is the part of speech of 'there'?)
1 and 3 are fine. 2 doesn't mean what you want it to mean!

"There" is simply an introductory word for this type of sentence construction. From what I've read, most other languages don't have an equivalent, and it's pretty much an idiom in English.
http://www.eslgold.com/grammar/there_is_are.html

It is not the subject of the sentence, but merely an introductory word.
http://dictionary.reference.com/browse/there
Scroll down here and read the Usage Note.

Related Questions

Errol is looking forward to excavating those. which word is the pro noun. “Forward: push forward, onward, do.” How can you apply this to your life? Some just look forward to the perspect of watching birds and animals,such as rabbits or deer,in thei... what are you looking forward to most in our study of Buster Keaton's "The General"? What do you inte... Forward to the following is the Hudson River School best known for? Poetry about the Northeast, pain... “I’m really looking forward to the concert tonight!” proclaimed Beth. “Me too, but I’m nervous. T... When is it OK to forward an email to someone else? You have considered whether it would violate... I’m really looking forward to it playing teenis Make that in a diff sentence What does the forward arrow in a chemical equation mean? 1) The reaction is reversible. 2) The re... What does the forward arrow in a chemical equation mean?(1 point) Responses The reaction proceed...