Have you tried google? It throws up this link [broken link removed] which lists Gordon Clarke's Sound Factory shop in Athlone, and plenty of other options.
Depends what type of musical instrument you are after, but you might be well advised to check out more specialised shops. A good quality second hand instrument might be a better deal than a brand new but lower quality.
The Sound Shop in Drogheda , not too far from Westmeath. http://www.soundshop.ie/index.php
Large showroom , stocks everything musical , very knowledgeable staff and excellent after-sales service.
I have no connection , just a very satisfied customer.
O' Neills in Glenamaddy? I hope they're still around. They certainly used to be the shop that musicians of trad, country & heavier went to for their musical instruments & equipment. They also sold to lesser mortals. I remember many, many moons ago, being bought an accordian there.