Is there a list of locations that you should avoid exploring to avoid breaking quests later on in the game? I like to randomly explore but find it annoying that I might ruin something else further down the line.

unfortunately no. all you could do is check every location on wiki for any quests related to the location and see if the quests have any bugs before going in and exploring it. too much effort if you ask me.

I really haven't come across any locations (like dungeons, tombs, barrows, caves) that would break a quest when i entered/cleared them. A lot of barrows have quests that start when you enter them. I think it's save to say, that you can go ahead and explore dungeons without issues. If the location is quest related, it's usually locked anyway and a key is required (like Saarthal and Mzluft for example as well as some Barrows/Tombs - Ysgramor's tomb etc).

The only issue I ran into with my very first character, is that I picked up Pantea's Flute, found in some Necromancer cave and then I couldn't start the quest later. All 3 instruments in the Bard quests are broken like that. Well, with Finn's lute, I could get the quest, but even then, these instruments will remain in your inventory. (The 3rd instrument is Rjorn's Drum). Just don't pick them up, when you come across them.

Some times, you will get quests that actually lead you to the same location, so I like to run that tomb/crypt etc just once LOL But heck, it sure doesn't break a quest, it's just laziness on my part. lol

I say, go for it, have fun, explore, don't worry about it.

So all Barrows can be explored freely? They're probably the highlight of the game do far. Massive and jaw dropping. Sorry for the spelling but when I got further down into Mizichital as I call it I felt as I really shouldnt go any further as it looked like I really shouldn't be there

There is a quest item at the end, yes, but I don't remember if I picked up "Grimserver" before I had the quest. Doesn't matter, you can explore that ruin, yes, definitely. Just be careful if you find a "named" item (like Finn's Lute, Grimserver, Wylandriah's Spoon etc) those are usually quest items. But yea, Mzinchaleft or other locations are free to be explored.

I love the Dwemer ruins. The noise, the steam, they are so alive, and creepy, and mysterious. I always try to imagine how life was, when the Dwemer were still around.

So yea, have at it. Not sure how much you have explored already, but I highly suggest you find the outpost of Septimus Signus (North of the College of Winterhold and make sure you are level 15 already). Get his quest and then go explore some cool locations.

grimsever is fine to pick up before you get the quest....

There is one place I can think of ..Cragslane Cavern. If you clear out that cave before starting a quest in Riften where it will require to kill 7 NPC's in the cave, they all won't respawn when you begin the quest. http://www.uesp.net/wiki/Skyrim:Cragslane_Cavern

Edit: Dang it spelling errors..always

Oh yea, I forgot about that one. Dwemer ruins though and Nordic Crypts are usually ok.