Random Utility Maximization (RUM) models of recreation demand are typically plagued by limited information on environmental and other attributes characterizing the available sites in the choice set. To the extent that these unobserved site attributes are correlated with the observed characteristics and/or the key travel cost variable, the resulting parameter estimates and subsequent welfare calculations are likely to be biased. In this paper we develop a Bayesian approach to estimating a RUM model that incorporates a full set of alternative specific constants, insulating the key travel cost parameter from the influence of the unobserved site attributes. In contrast to estimation procedures recently outlined in Murdock (2006), the posterior simulator we propose (combining data augmentation and Gibbs sampling techniques) can be used in the more general mixed logit framework in which some parameters of the conditional utility function are random. Following a series of generated data experiments to illustrate the performance of the simulator, we apply the estimation procedures to data from the Iowa Lakes Project. In contrast to an earlier study using the same data (Egan et al. [7]), we find that, with the addition of a full set of alternative specific constants, water quality attributes no longer appear to influence the choice of where to recreate.