Most likely the Void. The void is a "place" or rather, a plane of existence, apart from Eä. Tolkien gives so few references to this plane of existence that we can pretty much just make assumptions as to the nature of something that might come from that place.

One way to look at this is through a modern lens, and this is my personal headcanon, although I'm not sure the extent of Tolkien's knowledge into abstract cosmology, so this is obviously just my interpretation: Before the Big Bang, all of the matter and space in the universe was compressed into a tiny dot that eventually expanded into our universe. What was "outside" of this dot before this expansion? ...essentially nothing, not even space or time. A true void, at least to three dimensional beings like ourselves. The Ainur were not bound to Eä like we are, so they could traverse the void. If Ungoliant was a creature from that void, it explains her alien and powerful nature as she manifested on Arda.

Tom Bombadil, on the other hand, appears to be something rooted in the construction of Arda itself, and may have just been a part of the music by a particularly whimsical Ainur. A manifestation of the countryside that he appears to be part of. You could absolutely argue that Ungoliant was also some manifestation of something within Eä but outside of Arda, but as to why she would have power beyond the likes of Morgoth, makes me wonder if she is just something else entirely.