Yes, it's very close. Below is a map I did for another visitor. The Ashling is down near the R109 sign just left of The Old Jameson Distillery.
For a 2 days visit I'd recommend the following:
Guiness Storehouse
Old Jameson Distillery
Kilmainham Gaol
Royal Hospital Kilmainham (just opposite Heuston) nice gallery
Trinity College (Book of Kells is here)
Dublin Castle
Both Cathedrals
Also very close to you is the Zoo and The Phoenix Park.
We have the normal hop on-off busses, a Viking Splash tour (great fun, but does not allow hop on-off, so limited use to explore). There is also a Ghost Bust tour at night which I'd highly recommend.
You might take a look at the DublinPass which also included the Hop On-Off tour which will take you to all the sights around the city. Just check the things you'd like to do and see how it works price wise. Most of the museums and galleries are free, so keep them in mind also. There are versions (Freedom ticket and GoHop are two) that include the Airport bus to the city centre, might also be worthwhile.
Another alternative is to buy a Leapcard (like an Oyster card) (I think there is a tourist version also) which give you access to all the public transport in the city. It's capped to a max spend of €10 per day no matter how much you use it. This would allow you to go further afield like Malahide, Howth, Dalkey, though 2 days might be a bit short for those.
Although close to many attraction The Ashling is probably about a 30m walk into the main City Centre (Trinity College for example), the Luas (tram system) goes from Heuston so that might be a good option for you with the Leapcard.
Unfortunately Dublin is not cheap when it comes to Food & Drink, but there is plenty to choose from. I made some suggestions on a previous thread
here
If there's anything else ask away and welcome to Dublin
