Travelers interact with a large number and variety of products and services during their journeys. The quality of a travel experience depends on a whole urban mobility system considered in space and time. This paper outlines the relevant concepts to be considered in designing urban mobility. The goal is to provide a language and insights for the early stages of a design process. A literature review sheds light on the complexity of urban mobility from technical, socio-technical, and user experience (UX) perspectives. Observations of experiences in urban areas provide data for describing and understanding travel experience patterns and issues. The paper proposes a conceptual model to describe and analyze different facets of traveler experience, and categorizes problems that travelers face when they interact with an urban mobility system. A case study is reported illustrating the use of the conceptual model in identifying travel problems for a demand-responsive transport (DRT) service.