Do they mingle with the elves? Do they have their own little kingdom somewhere where they fraternize amongst themselves? Or do they stay in Valimar atop the mountain where the Valar are?
It depends on the Maia in question.
There are surprisingly few references to the Maiar in The Silmarillion. While it seems likely that many dwelt in Valmar, we have explicit knowledge that at least two lived in Lórien:
Melian was the name of a Maia who served both Vána and Estë; she dwelt long in Lórien, tending the trees that flower in the gardens of Irmo, ere she came to Middle-earth. Nightingales sang about her wherever she went.
Wisest of the Maiar was Olórin. He too dwelt in Lórien, but his ways took him often to the house of Nienna, and of her he learned pity and patience.
The Silmarillion II Valaquenta "Of the Maiar"
Considering that not even all of the Valar dwelt in Valmar (Mandos is a bit of a loner type, and prefers his halls, and Ulmo likes living at the bottom of the ocean), it seems exceedingly plausible that other Maiar also live in various parts of the Undying Lands.
They mostly lived in Val(i)mar together with the Valar.
From Tolkien Gateway:
Valmar or Valimar was the city of many bells in the heart of Valinor where many of the Valar and Maiar dwelt.
And from Wikipedia:
In east-central Valinor at the Girdle of Arda (the Equator of Tolkien's world) is Valmar, the capital of Valinor (also called Valimar or the City of Bells), the residence of the Valar and the Maiar in the realm of Valinor. The first house of the Elves, the Vanyar, settled there as well.
Curiously I couldn't find any primary source for this, although I had a search through the Silmarillion looking for a relevant passage.
It makes sense to assume that they lived with or near the Valar they were associated with.
For example, Ossë and his spouse Uinen lived in the seas, as they were associated with the Vala Ulmo who dwelt in the ocean depths.
Varda's maiden Ilmarë lived in her and Manwë's mansion on Taniquetil, and I'd imagine that Manwë's herald Eönwë wasn't far from it.
Curumo, who came to be known in Middle-earth as Saruman, belonged to Aulë the Smith, and so logically would have lived in or near Aulë's halls. Mairon, who later became known as Sauron, was also originally of Aulë's people.