Ariadne's Penthouse is very central, next to Syntagma Square, the shops on Ermou St., the tourist areas of Acropolis, Plaka, Temple of Zeus, and of course the great restaurants on Xenophontos and Apollonos streets.
You have everything you need at your doorstep, including the trendy bars and cafes on Kolokotroni St. and the classy boutiques of Kolonaki.