As he travels around Cyrodiil, Alval Uvani can be found at the following locations, on the following days:
Morndas/Tirdas -- Bravil -- The Lonely Suitor Lodge
Middas/Turdas -- Skingrad -- The West Weald Inn
Fredas/Loredas -- Bruma -- Olav's Tap and Tack
Sundas -- Leyawiin -- Alval Uvani's House (rented property)
Keep in mind that there may be some variation based on the time it takes for him to get to the different cities.