1. You can enjoy delicious food in London.

2. In London, you can enjoy delicious food.

(Are both the same? In #1, what does 'in London' modify?)

3. You can visit many traditional houses in Chicago.

4. In Chicago, you can visit many traditional houses.
(Both are the same. In #4, 'In Chicago' is an adverbial phrase. However, in #3, what does 'in Chicago' modify? Is it an adverbial phrase as in #4? Or is it an adjective phrase modifying 'houses'?)

they are all adverbial phrases. They are all modifying the verb.

I guess syntactically they could be adjectives working on the direct objects, but I think the sense is clearly that the enjoying and the visiting are what is in London and Chicago.

Yes -- adverbial. They answer the question "where?"

Both #1 and #2 convey the same meaning, which is that there is delicious food available in London. The phrase "in London" in both sentences is an adverbial phrase that provides information about where you can enjoy the food. It indicates the location where the action of enjoying food takes place.

In sentence #3, "in Chicago" modifies the noun "houses." It serves as an adjective phrase, specifying the location of the traditional houses you can visit. In this case, "in Chicago" acts as an attributive prepositional phrase, providing additional information about the noun it modifies.

In sentence #4, "In Chicago" is also an adverbial phrase, functioning as an adverbial modifier, just like in sentence #1. It provides information about the location where the action of visiting the houses occurs.

To summarize:

- In sentences #1 and #2, "in London" functions as an adverbial phrase, indicating the location of enjoying food.
- In sentence #3, "in Chicago" acts as an adjective phrase, modifying the noun "houses" to specify the location of the houses.
- In sentence #4, "In Chicago" is an adverbial phrase, specifying the location of the action of visiting the houses.