In this paper, we consider the problem of designing personalised museum visits. Given a set of preferences and constraints a visitor might express on her visit, the aim is to compute the tour that best matches her requirements. The museum visits problem can be expressed as a planning problem, with cost optimization. We show how to bound the number of steps required to find an optimal solution, via the resolution of an instance of the shortest complete walk problem. We also point out an alternative encoding of the museum visits problem as an optimization problem with pseudo-Boolean constraints and a linear objective function. We have evaluated several constraints solvers, a planner and a tailored solver on a number of benchmarks, representing various instances of the museum visits problem corresponding to real museums. Our empirical results show the feasibility of both the planning and the constraint programming approaches. Optimal solutions can be computed for short visits and ``practically good'' solutions for much longer visits.