travel itinerary starting in Llangollen

For what you are wanting to do, Llangollen isn't the best of choices, particularly if you are wanting to do everything by public transport, which isn't brilliant. Snowdon would be a nightmare! Maybe you need to rethink...

LLangollen is a lovely town - have a look at the town trail leaflet here.

https://www.northeastwales.wales/wp-content/uploads/2022/03/llangollen-town-trail.pdf

You could make a really special graduation gift for your daughter based on the immediate area.

You do have a (very) ruined castle overlooking Llangollen - Castell Dinas Bran and it is a good walk from the. It is quite steep though. information and map here.

http://www.gps-routes.co.uk/routes/home.nsf/RoutesLinksWalks/castell-dinas-bran-walking-route

There are also the ruins of the lovely Valle Crucis Abbey, again walkable from Llangollen

http://www.cistercianway.wales/directory/valle-crucis-strata-marcella/valle-crucis-llangollen/

A short walk from the town is the old timber frame Plas Newydd House - go and have a cake in their tea room. This is a short wa

https://www.denbighshire.gov.uk/en/leisure-and-tourism/museums-and-historic-houses/plas-newydd-llangollen.aspx

Do a canal boat trip across the Pontcysyllte Aqueduct,

https://www.pontcysyllte-aqueduct.co.uk/business-community/boat-trips-boat-hire/

Or else do a horse drawn canal trip from Llangollen.

https://www.horsedrawnboats.co.uk/

Go for a ride on the LLangollen Railway.

https://llangollen-railway.co.uk/

You really would be better off hiring a car for getting around north Wales. One a good road trip from Llangollen is this route > Bala > A494 Dolgellau (use by-pass) > Barmouth > Harlech (Castle) > Portmeirion (Italian style village) near Minffordd then return east via Maentwrog to Bala & Llangollen.

To reach Snowdon from Llangollen follow A5 NW to Betws-Y-Coed > Capel Curig and A4086 to Llanberis.

Another good day trip is the same route to Betws-Y-Coed and then A470 northward to Bodnant Gardens and then on to Conwy (Castle) and Llandudno.

I guess the best thing to do would be to take the train from your arrival airport to either Chester (well worth seeing) or Shrewsbury (Worth a look) in order to hire a car. Llangollen is not on the rail network - nearest stations are Ruabon or Chirk. A tourist steam railway does exist at Llangollen.

Look on google maps and check out street view to see the kind of roads.

While in Llangollen stop to see the nearby Pontcysylite Aqueduct. Pretty i there’s ting feat of engineering.