After many years of near-civil war, which only ended in 2005, Banda Aceh is very new on the international travel scene. There still isn't much infrastructure, but there is enough to make the city and surrounding areas easily accessible. The city itself will appeal to those looking for some place a little “off the map” where they can relax and enjoy a slower pace without necessarily having to do a lot of sight-seeing.
The Rumoh Aceh traditional style house in the grounds of the Aceh Museum
There isn't a lot to see in Banda Aceh. It can seem like the main sights are the fading memorials to the 2004 tsunami, and the rest are not what I would call spectacular or impressive. However, that said, I found the city to be quite an enjoyable place to simply pass the time, sitting in one of the many coffee shops, sipping the strong black local brew, and maybe taking in a little conversation with one of the friendly Acehnese, who despite a very limited amount of English were among the most outgoing Indonesians I've ever met.
Fishing Boat on a House
There isn't a particularly good time of year to visit Banda Aceh, although you might wish to avoid the wetter months of October to December. Given the conservative Muslim nature of the entire province, you might also want to avoid the fasting month of Ramadan, since many restaurants might be closed for the entire day. The sights of the city (see map) can be seen in a full day of sightseeing.
Unfortunately, there aren't any hotels I can recommend in the city center, close to the sights, so you'll need to either engage a car and driver, which you can do through your hotel, or use becaks to get around. Banda Aceh isn't much of a destination for foodies, but you definitely don't want to miss one of the city's distinctive local coffee shops.
When planning your day, it's worth noting that many museums and businesses close for noon-time prayers, which can last from around noon to around 2:00 pm. Note especially that on Friday, everything closes for noon prayers. The streets will be almost deserted during prayer times.
Lastly, you should remember that Aceh is perhaps Indonesia's most conservatively Muslim province. You won't find much alcohol on sale, especially outside of hotels, and women especially are encouraged to dress appropriately.