i would stay near Menai Bridge for accommodation!
the village is nice and has lots of different pubs and eateries including a michelin star restaurant - but i doubt you will be able to get a booking that soon ( i think december 18 is the soonest) anglesey arms and victoria hotel are both in the village, carreg bran as said earlier is just by the Britannia bridge (have a look for the lions) about a mile from menai and half mile to llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch in the other direction where there i is a couple of pubs and the pringles shop and railway station which gather a lot of interest.
Beaumaris is a 15 minute drive and is lovely to stop in at on the way to penmon (lighthouse, priory and dovecote) with good pubs, food, castle and pier (fishing trips from here or tours of puffin island)
newborough/llanddwyn 20mins the other way is a truly outstanding beach and forest.
the coast up from there will bring you to Valley RAF base - if your into planes?
on the rhosneigr for kite surfing and little little tourist cafes,
over to holyhead will bring south stack lighthouse and lot of seabirds - not much in the town unless you like ferries.
over toward amlwch will bring parys mountain - an old copper mine - looks like your on mars!
moelfre will bring an lovely fishing village
mynydd bodafon on the way back to benllech is really pretty.
lligwy, benllech and red wharf bay are all popular tourist spots with some good cafes and beach huts.
then you are nearly back to beaumaris but Llanddona beach is worth a walk on for the miles of beaches and 25% & 35% hills to get there and back.
lots of places for you to google there but as per OP i would stay near menai if possible - the island is only 25miles across and you can get anywhere within an hour... remember the country lanes
also it is a better base if you do want to go exploring in snowdonia.
any questions feel free to ask away
ben
#edit check my profile pic for a clue to where i live