Becoming thane of every hold is fun for roleplay makes you known by everyone everywhere you go. If using archery in my build I sometimes equip myself with fur or skaal armor and go on long hunting journeys around skyrim with only a bow, all the arrows I currently have, a sword/axe, a few poisons/potions and read nearly every book I come across for a break, and is sometimes quite interesting. Stopping at local Inns for a drink, some food and a bed to sleep in is also fun to roleplay. It's great fun hunting and allows you to explore more of skyrim. other than just following the quest marker for hours on end then ending up with nothing to do and scrapping the build.
I play on console so I can't use mods to add new or more pre-existing animals but there's always a deer/elk or some other creature lurking around.. I usually start off in one location and go wherever I please, or if I'm doing a quest I'll get into my hunting gear and hunt my way to the quest marker. If I know a cave that has animals in it I'll usually clear it out but I've had them few times where I walk into a cave with a bear in it and end up being attacked by the falmer and having to escape!
I would recommend not fast traveling at all unless its by carriage, this allowed me to experience and discover new locations that I've never seen before in Skyrim.