The short answer to the question of "where" Rebecca went is, We are not told. However, that is not necessary.
The Hebrew word used here is הָלַךְ (halak), and in this case the verb is Qal, Consecutive imperfect. This verb is extremely common as it occurs more than 1500 times in the OT and simply means: to go, or to come or to walk.
Significantly, in this case הָלַךְ (halak) is immediately followed by לִדְרֹ֥שׁ (liḏ·rōš), which is a Preposition + Verb - Qal - Infinitive construct. Thus the phrase means that Rebecca, "went to inquire" of the LORD. This is quintessential Hebrew idiom. No specific geographical or physical location is implied, it is just Hebrew idiom.
Thus, the meaning is that Rebecca went to God in prayer. In more modern idiom we might simply say, "Rebecca prayed". However, it is quite possible that she did go to a person, or went to the family altar, or went to her private quarters (eg bedroom), etc, in order to do the praying/inquiring (eg, 2 Kings 22:13, 2 Chron 34:21) but that is not essential to the semantics and grammar here.
The same construction is used in 1 Sam 9:9, "went to inquire" but in that instance, the location was the seer (Samuel). According to BDB, the verb, הָלַךְ (halak), followed by another infinitive verb is used in the following places:
a. followed by Infinitive of purpose (with לְ) Genesis 25:22; Genesis
31:19; Genesis 37:25 (all J E) Numbers 14:38 (P) Numbers 24:1 (JE),
Judges 8:1; Judges 9:8,9,11,13 + often; especially לִקְרַאת ׳הּ go to
meet Joshua 9:11 (JE), 2 Samuel 19:16; 1 Kings 18:16 (twice in verse)
+; sometimes with hostile sense 1 Samuel 23:28; 1 Kings 20:27; 2 Kings 23:29; also לָּשּׁובּ ׳הּ go to return, Exodus 4:21 (RV go back),
compare also שּׁובּ לָּלֶּכֶּתּ return again Ecclesiastes 1:7;
Ecclesiastes 5:14; לָּבּוֺֿ ׳הּ go to come (enter etc.) Jeremiah 41:17
compare 2 Chronicles 26:8.