In the competitive facility location problem, a newcomer firm optimally locates its facilities and offers a product that is a substitute for those of the already located competitors, aiming at maximizing its market. Usual facility location models assume single-stop or single-facility trips. However, when products are non-homogeneous substitutes, customers may want to compare the products before making a decision (comparison-shopping). Moreover, decisions are often made sequentially as facilities are visited. We model for the first time, sequential customers' decisions in multi-stop trips, represented using a nested logit rule. Customers make decisions at the place of origin (which facility to visit first), at the first visited facility (whether to buy, or not, or to continue comparing), and at the second facility visited (whether to purchase or not and in which facility). To adequately represent the drive to compare, we include in the customers' utility the value of the gathered information, and the disutility of visiting facilities without purchasing. We propose a linear formulation with an efficient branch-and-cut approach. We analyze the location patterns in randomly generated instances, as well as in a case study on municipalities in Spain. The three-level nested, two-level nested, and multinomial logit rules are compared.