Mannheim is a major north-south train artery and has a well-developed public transportation network, including trams and buses. Public transportation can get you almost anywhere in the Mannheim - Ludwigshafen - Heidelberg area. The Mannheim train and bus stations are right next door to each other. Frankfurt International Airport can be reached by bus or a 30-minute ride on ICE (Inter-City-Express train).
A number of international car rental brands are in the city, several of them conveniently located at the main train station.
Bikes are a convenient way of getting around a city where the first bicycle was put together in 1817. VRNnextbike has rental stands conveniently located near bus and tram stops and train stations. It allows you to pick up a bike in one city in the region and return it in another. The rate is € 1 for every 30 minutes with a daily maximum of € 9. Sign up for free at the website or on the App.
The Mannheim/Ludwigshafen tramway network has been around since 1878 and provides extensive service in the two cities, including to Heidelberg. Fares are based on how many "wave" or "combs" you cross to reach your destination. Options include a single ticket, "square" ticket around the central area, multi-ride, day (1, 3 or 7). Automatic ticket machines provide instructions in English.
Taxis are metered and can be picked up at taxi stands or called by phone. You'll pay for comfort and convenience, but the taxi industry on the whole is well regulated in Germany where on-demand shared ride services have encountered legal challenges.