The centre of Armenia is compact and walkable — from Plaza de Bolívar you can reach most central restaurants, the food market, and the main shopping streets on foot. The city has no metro and is hilly enough in places that you will want a taxi rather than a bus for longer trips.
Taxis are cheap, metered, and widely available; central rides are usually 5,000 to 9,000 pesos. Uber and Didi operate (legality is grey but use is common) and tend to be a bit cheaper. For trips to surrounding villages — Salento, Filandia, Calarcá, Quimbaya — the cheapest option is a colectivo from the main terminal, with frequent departures throughout the day for around 5,000 to 12,000 pesos each way.
For the Cocora Valley specifically, you take a bus or colectivo from Armenia to Salento, then a jeep willy from Salento's main plaza onward to the trailhead.