I'm so sorry to hear your news but I'm loving your positivity about planning a trip to Anglesey.
I've lived most of my life on Anglesey and am not in the least bit surprised how many people love coming back year after year. I'll try and go through the suggestions already made in terms of how wheelchair friendly they are for you.
Beaumaris - lovely town, lots of independent shops, small pier, plenty of pavements near the sea to get the air. The main church is also worth a visit, it might involve a couple of steps getting in though, if you could manage that?
Penmon Priory - a few miles from Beaumaris, most accessible by wheelchair and a flat path to St Seiriol's Well nearby. A bit further on down a toll road is Penmon Lighthouse and the views of Puffin Island, Llandudno and the mountains on the mainland.
Red Wharf Bay - drive down a narrow twisty lane but all flat when you get to the bottom. A few cafes/restaurants, The Ship Inn is quite old and has a lovely outside eating area, weather permitting.
Benllech beach - lots of parking and a good pavement overlooking the beach
Moelfre - lovely little old fishing village, nice pub overlooking the beach, accessible. The lifeboat musuem is worth a visit too and also has lovely views out to sea, good spot for seeing dolphins etc
Lligwy beach - you can drive to the car park behind the beach, lovely views
Amlwch Port - drive down to the port, it's where all the boats used to dock when loading up the copper from Parys Mountain
Parys Mountain - drive south from Amlwch towards Llanerchymedd and you get can a feel for the place just from the car
Bull Bay - laybay just before the village as you come from Amlwch, good views out to sea and you can sometimes see the Isle of Man (on a very clear day 
)
Llanbadrig church - car park adjacent to the church, fairly decent pathway into the churchyard and maybe a step or two into the church. Worth a visit inside and the location is stunning.
Cemaes Bay - car park overlooking the main beach. The jetty is wheelchair accessible to see the fishing boats. The Harbour Hotel has a bar/restaurant with great views over the beach and village.
Cemlyn Bay - one of the quieter spots on the island, great for bird-watching, car park next to the lagoon.
Porth Swtan/Church Bay - a twisty road down to the hamlet, good parking and a couple of places to eat. The beach is not wheelchair friendly but lovely views over to Holyhead, also great views on the drive down.
Melin Llynon/Llynon Mill - fully restored working windmill, the only one in Wales. Only the ground level would be accessible by wheelchair but they also have a lovely tea-room which has a stair lift. You can also buy bread and cakes made with wheat from the mill. They have also constructed two Iron Age roundhouses nearby which are a fascinating glimpse into the past.
Penrhos Nature Reserve - between Valley and Holyhead. Lots of good paths through the woods, all wheelchair accessible, very popular with dog walkers.
Holyhead Breakwater - it is possible to go right to the end of the breakwater, the longest one in UK. Might be a bit hard going pushing a wheelchair though. Also Newry beach overlooks the breakwater, it's not much of a beach but great views, lots of parking and good pavements the whole way along. Lovely cafe/restaurant at the old lifeboat station, wheelchair accessible.
South Stack Lighthouse - you can drive right to the end of the road to a car park which overlooks the lighthouse (and the hundreds of steps down to it). Great place for views, it's usually windy there so it blows away the cobwebs. Just before the end of the road is a cafe run by RSPB, wheelchair friendly and lovely views out to Trearddur area of Anglesey and across to Lleyn Peninsula.
Take the back road from South Stack towards Trearddur Bay, lots of small coves along the way with places to stop and admire the views.
Trearddur Bay - excellent promenade above the beach. The Black Seal is the best place for views over the beach.
Rhosneigr - dead quiet in winter, heaving in summer. It's not the best place to get near to the sea in a wheelchair but lots of cafes etc.
Aberffraw - pretty little village with its old bridge and you can drive down (another) narrow lane to see St Cwyfan's Church (the church in the sea)
Newborough Beach and Forest - there is a fee to get into the forest and whilst the beach is stunning, and Llanddwyn Island is spectacular, I'm not sure it's very wheelchair-friendly.
Plas Newydd - owned by the National Trust and mostly accessible.
Menai Bridge - lots of independent shops and cafes. There is a footpath down to Ynys Tysilio/Church Island. It's very steep in parts but it is definitely doable (I speak from experience). Well worth the effort to see the Menai and Britannia Bridges from a different angle. Good chance of seeing red squirrels too.
Please remember in Anglesey we can, and often do, have 4 seasons in one day so pack clothes for all possibilities
@BitOfFun, I think I've gone on long enough for today but if you have any questions then please feel free to ask 