Both approaches can be used. Approaches are different. But I suggest you to use travel cost method but again this depends on the objective of the study and literature can guide you better
So, unless I misunderstand the concept of 'travel cost' I assume that you are measuring the 'economic value' of a site - I confess I am unclear as to what you mean by 'recreational value' in this sense. Surely such values, which for me would include health and wellbeing, can not be measured by studying travel costs? You need to be very clear about what you are measuring and WHY - it is the why? question that should drive your decision.