Rhodri's pater, Cuprincus, gifts him with a size +2 laboratory with Superior Equipment, and moves it in for him with The Ambulatory Laboratory. Because the set-up of the lab is identical to the one Rhodri slaved away in during his apprenticeship, Rhodri will not need to spend any time refining this lab for his own use. If he wants to take over an existing lab, though, that will take time, and if he wishes to give this lab to another magus, they will have to spend time refining it before they can use it without penalty. He would still need to pick someplace for his sanctum before the lab can be moved to the covenant, though.
Inside the Mercer House, there is a size +2 laboratory with Superior Equipment, which Aequi has been squatting in at the sufferance of House Mercere (unbeknownst to any outside of House Mercere). Attravere, as resident Magus Merceris, has the right to claim this laboratory as his own sanctum, and should he wish to do so the lab will be stocked with Priceless Ingredients (and all upkeep for this laboratory is covered by House Mercere, as it is Mercer property and not a part of the covenant). However, if Attravere wishes to set up a sanctum elsewhere, he can do so without any negative repercussions from the House. (Your predecessor didn't live here, after all; with the exception of Aequi and another transient non-Mercere magus indebted to the House, this lab has been empty for almost a century. And yes, the Mercer House was here long before a covenant set up around it.)
There is a guest laboratory on the second floor of the tower (below the library). Currently it is being used by Lamentus' apprentice, Shmuel, but by nature of being an apprentice, he can be bumped by any full magus should someone want to make it their sanctum. It is a standard laboratory with the exception that it is size +1.
As reminders, Aislinn's laboratory, Justinius' laboratory, and Maribus' laboratory have been left abandoned and are up for grabs.
*Aislinn's laboratory is outfitted with Flawless Equipment and is specialised for Auram and Ignem, but it is protected by a giant fire elemental and an invisible spirit of some sort (probably an air elemental). V/F: Unknown. Greater Guardian for sure, though 
*Justinius' laboratory has not been seen by any but the couple themselves. His skill at Intellego was legendary, and he was known to be more than passing fair with Terram as well. He had been seen entering and leaving his laboratory by melding into the stone itself. V/F: Unknown, though he almost assuredly has Flawless Equipment as well, having been a glassworker of some renown.
*Maribus' laboratory is encased in a cube of translucent crystal, which lies at the bottom of the river. Attravere knows that it is mobile, and can be moved using an enchanted orb within it, but he does not know how to activate that effect. Maribus used the mobility of his laboratory to facilitate shipwrightery. The lab itself has Flawless Equipment and is stocked with Faerie Ingredients supplied by river nymphs, and includes a vis source-- a distillation apparatus that automatically extracts 1 pawn of Aquam per season from the river. Moving the lab out of the river would negate the vis distillation, and probably the faerie ingredients too. The orb also has the ability to drain water out of the lab, and keep it pumped with fresh air; in the interests of keeping his apprentice alive, Maribus DID teach Attravere how to activate that particular effect. V/F: Natural Environment, Underwater, Mobile, Flawless Equipment, Faerie Ingredients.
Little William offers to go check on Erro at Leona's laboratory, only to discover that the beast-magus seems to have moved on; thus, Leona's lab is up for grabs as well, though there are complications. The faerie forest exudes a Mentem effect causing travellers to get lost-- William informs the council that guests in good standing with the local faerie court are immune to the effects. Additionally the lab itself is under the effects of The Shrouded Glen with 26 points of penetration. Guillaume is immune to it, and it cannot penetrate Attravere or Rhodri's parmae, however, the lab is specialised for Herbam, Animal, and Corpus, AND is protected by three giant animated trees, a talking bear, and a talking gyrfalcon... and that's on top of the horde of faerie polecats who live here. V/F: Natural Environment, Living Quarters, Dedicated "Building," Faerie Ingredients, Flawless Equipment, Greater Horde (faerie polecats), Shrouded, Greater Focus: Statue (Corpus).
Hence, mid-January!)
Shmuel glares daggers at her at every meal, and makes a point to correct all of her Latin errors and some inconsistencies in Magic Theory during Hermetic discussions (there's nothing more obnoxious than a precocious eleven-year-old with a +5 Int, 6 in Latin, and more Magic Theory than most Bonisagi). And just when Sinmore looks like she's about to blow her top, Shmuel makes some comment about how his pater is one of the oldest and most powerful in the Tribunal: "He was alive in William the Conqueror's day. He's oldest second only to Iudicium...maybe. I think. Actually... how old IS Iudicium??? Does anyone actually know?"
In that case... he does break a sweat, and you manage two touches on him, as opposed to the eight touches he scores on you.