Parking is widely available but expensive. You could use the St Stephen's Green shopping centre car park which is less than five minutes from Harcourt Street. If, by any chance, you're a garda you could simply park on the pavement or any double yellow line you happen to see free.
Assuming you're not howver, you might be as well to park your car for free in the Phoenix Park on the approach to Parkgate Street and get the bus from that street (or the Luas from Heuston) into town as far as O'Connell Bridege. From there, it's about a 10/15 minute walk to Harcourt Street.
You'd need to allow about an hour to Harcourt Street from the time you leave Parkgate Street. Don't know how long it would take to get to PArkgate Street from Athlone, though.