I use Wordpress and Youtube for vids. No it's not perfect but it works easily. You can place vids in your posts while Youtube is your media center.
Photos can be held in WP or for ex. Flickr if you want a still pic video center.
It sounds as though you are planning a rather long and/or extensive trip log. If so there will be as many people arriving 'late' to the blog as following in real time. In either case, if you put the entire trip in its own blog there are enough facilities in WP to allow you & users several ways to explore for content as well as for you to hi-lite certain aspects of the trip.
Don't fight what can't be done, defeat it by doing what can be done.