I'm sorry, but I would need to know specifically what you are referring to by "grammatical type." My only clue comes from one of your previous questions (https://www.wyzant.com/resources/answers/164061/write_a_two_to_three_paragraph_at_least_200_words_personal_experience_essay_in_which_you_use) where you also mentioned grammatical type in the context of indicating that the essay you needed to write had to include "at least one sentence containing parallel structure" and you needed to "[u]nderline the parallel elements and identify their grammatical type." So notice here that the "grammatical type" seems to be concerned with the "parallel elements" within that "one sentence containing parallel structure," not the whole sentence itself or whatever other sentences containing parallel structure you optionally could have also written.
So taking the second sentence you give here, which I'm pleased to see you adopted from Roland M.'s fine suggestions in answering your original question, note that Roland himself wrote, "As far as parallel structure is concerned, you could say something like: I like to take hikes and to look at the fall leaves." That is, Roland suggested you use two infinitive phrases, namely to take hikes and to look at the fall leaves, so called because both have the grammatical structure called an infinitive, i.e., to plus the invariable, untensed form of a verb.*
Now, your first sentence, "As a person who lives in Roanoke, Virginia , [sic] I like to take hikes in the mountains," also has the infinitive phrase to take hikes in the mountains but no other one, and neither does it have any other grammatical structure that is repeated and thus there is no kind of parallelism. But looking back again at Roland's answer to your original question (and I see now that you actually followed up on it and asked specifically about the grammatical type), I see that he suggested
(The following should be indented, but I've noticed that indenting function doesn't seem to work properly in these WyzAnt answers:)
As a person who lives in Roanoke, Virginia, I like to take hikes in the mountains (or whatever it is that you like to do). This phrase, alone begins with a modifier (as a person) and includes the relative pronoun who. It also includes the personal pronoun I.
So one way to characterize As a person who lives in Roanoke, Virginia is that it is an appositive phrase that as a whole modifies the subject of the main clause, namely I; in other words, you are indicating that "I am a person who lives in Roanoke, Virgina" in addition, and actually relevant, to the information that "I like to take hikes in the mountains." And who lives in Roanoke, Virgina is a relative clause (note that Roland correctly identified who as a "relative pronoun") which modifies person.
*Actually, the latter itself is often called the "infinitive" of a verb, whereas such a verb preceded by to is termed the "to-infinitive." Just a little aside that fulfills little other function than to potentially confuse you and/or show off my erudition.