Villach's old town is compact and thoroughly pedestrianised — you can walk from the train station to any point in the historic centre in under ten minutes. Most of the main sights, the Hauptplatz, the churches, and the museum are within easy strolling distance of each other.
Cycling is the best way to expand your range. The city has a well-developed cycle path network that connects to the Drau valley cycle route (Drauradweg), one of the major long-distance cycling paths in the Alps. The path south toward Warmbad Villach (about 4 kilometres) and north toward Vassacher See is easy and well-signed. Bike hire is available at several points in the city including near the Hauptbahnhof.
Local buses (operated by Stadtwerke Villach) cover the urban area including routes to Warmbad. For day trips to Faaker See and the surrounding villages, regional buses are adequate but a car is more flexible. A car is also useful for the Villacher Alpenstrasse, which is not served by public transport.
Taxis and rideshare are available but not heavily used in a city this walkable. For the railway connections to Wörthersee, the train is both faster and more enjoyable than driving — the line runs along the lake's northern shore with good views.