You'll find banks and ATMs along Jirón Lima (aka Pasaje Lima), as well as at Hotel Casa Andina, Jr. Independencia 185. Banks include Banco Continental, at Jr. Lima 400, and Banco de Crédito, on the corner of Jirón Lima and Jirón Grau. Money-changers can generally be found along Jirón Tacna, where most bus stations are located, and at the market near the railway and Avenida de los Incas.
For those crossing into Bolivia, the Bolivian Consulate is located at Jr. Arequipa 120 (tel. 051/351-251). North Americans, Europeans, New Zealanders, and Australians do not need a visa to enter Bolivia, but the border is a historically problematic one (it was closed in 2005 during the widespread strikes that paralyzed parts of Bolivia), so you might need to check on the status of the crossing before traveling to Bolivia.
In a medical emergency, go to Clínica Puno, Jr. Ramón Castilla 178-180 (tel. 051/368-835), or Hospital Nacional, Av. El Sol 1022 (tel. 051/369-696). The tourist police are located at Jr. Deustua 538 (tel. 051/352-720).
Pretty fast Internet connections are available at Qoll@internet, Jr. Oquendo 340 (Parque Pino), where you can make inexpensive international calls; rates are S/2 per hour. A nice, quiet spot for surfing the Internet is behind the cafe at La Casa del Corregidor, Deustua 576 (tel. 051/351-921). Other Internet cabinas are located along Pasaje Lima. Puno's main Serpost post office (tel. 051/351-141) is at Moquegua 269. The Telefónica del Perú office is on the corner of Moquegua and Arequipa.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.