Bahir Dar grew around a Jesuit settlement, founded in the sixteenth or seventeenth century, from which time the Pedro Páez building dates. One of Emperor Haile Selassie's palaces is near the city, and the Emperor considered moving the national capital to the town. The palace is an impressive architectural work of its time. Facing Lake Tana it provides a beautiful, picturesque scene of the Blue Nile. You cannot actually go inside the palace, or see it very well. Nevertheless, there are “tour guides” who hang out around the site and will tell you a few facts for ~100 birr per person. It’s a nice nature hike...sort of.
© OpenStreetMap contributors
Huge monument with waterfalls going to Blue Nile. Include a museum with pictures.
Some of the world's oldest churches and monasteries are on islands in Lake Tana. There are lots of boat tours available to the monasteries. Entrance at each monastery is 100 birr as of 2016. The tours range from 2 to 12 hours long and can be booked through your hotel, by contacting a guide directly on WhatsApp, or by one of the many touts in the city. They can organise a boat tour for half a day and a trip to the Blue Nile Falls for the other half of the day, which should cost no more than 400 birr per person. You can do it much cheaper by chartering your own boat and visiting only the islands you want to see and also getting a local minibus to the waterfall (as of 2019, 1500 birr seems like a good price for a custom, private half-day tour for 2 on Lake Tana with a well-rated guide). At some of these monasteries, women are not allowed to enter. Be cautious and aware of the traditions and rules of the Ethiopian Orthodox church when you visit. These churches are unique to Ethiopia, but they tend to be expensive and the tours are overrated. The boat trip on the lake is nice, but there are better examples of rural churches elsewhere in Ethiopia in a more pleasant and less touristy environment. As part of a boat tour, you may also swing by the 'Head of the Blue Nile', where the river flows out of the lake. There's a good chance of spotting a hippo or two pop up their heads. Otherwise, it's nothing too spectacular.
Tis Abay in Amharic
A once spectacular sight that has been ruined by the building of a hydro-power dam. In rainy season (May to Sep) there is a decent flow but in the dry season the falls are pretty minimal and probably not worth suffering for 2.5-3 hours on bad gravel roads. If you take the bus, ignore anyone in the village who insists that the last bus back to Bahir Dar will be full and wants you to pay them to hold a seat, or that the last bus has already left but they can offer you an amazingly expensive taxi ride. There are plenty of buses back to Bahir Dar, the last one leaves at 17:00 or later, and the bus conductor will find a seat for you! You can also arrange for a tour to the falls through your hotel. If you visit during rainy season, be aware that paths are very muddy (deep mud) and bring adequate shoes. A nice alternative to the standard day trip, especially if you'd like to experience sunset and sunrise at the falls, is an overnight stay at Blue Nile Camping, right at the top of the waterfall.