Ipiales is a seedy border city, but if you have some extra time to kill, there are a few plazas to visit in town. The real attraction, however, is about 15 minutes away.
Plaza La Pola has a monument to Policarpa Salavarrieta, a Colombian revolutionary heroine, and the blue and white Iglesia de San Felipe.
There is also Plaza de la Independencia. It has a few colonial buildings surrounding it as well as a nice cathedral.
Santuario de Las Lajas is the real reason people come to Ipiales. This beautiful church sits in the middle of a gorge. Read about it here. Taxis cost COP$8,000 to travel to Las Lajas from Ipiales and can be shared between four people for COP$2,000 each. Give yourself at least an hour to admire the scenery in addition to the 15 minute rides there and back. Taxis are easy to find going back to Ipiales, so there is no need to ask one to wait for you.
Travelers going between Colombia and Ecuador by bus will probably have to pass through Ipiales. There are a few cheap hotels near the bus terminal if you need to stay overnight. Buses travel to Ipiales from Cali (11-12 hours), Popayán (9-10 hours), and Pasto (2 hours). I’ve taken an overnight bus from Cali with TransIpiales and a daytime bus going the other way with Bolivariano. Both companies have good service but beware – book your tickets early for weekend travel.