Shauna,
It will take some time to collect your luggage and clear Immigration in Dublin. I'd suggest taking a Taxi to your Hotel. There's a queue outside the airport for Taxi's and you won't have any trouble finding one - there are LOTS of them. Your Driver will probably be quite talkative, so you'll get up to speed on the local news straight away!
Which area is your Hotel in? Under the circumstances, I'd "play it by ear" and see how your Grandmother feels at the time. If she's really jet lagged, a short nap might be in order?
The Hop On / Hop Off Bus tour would be a good way to get some idea of the layout of the city. As I recall, one of them stops near the Kilmainham Gaol, and that's definitely a worthwhile site to visit (if you're not too tired). I have "mixed feelings" about the Guinness Storehouse. It was interesting to see (and of course have a "free" pint), but I wouldn't place a high priority on it.
You might like to do a bit of a walkabout in the Temple Bar district, just to have a look. For other sights, I imagine your tour will cover those (which tour are you taking?).
Happy travels!
