I'm still working on my first character, and decided to choose a Breton, which is what I've played in the other Elder Scrolls Games.
I like using magic, but still think that it's a bit bland and underpowered (As many many other people have been saying) so I've been trying to mix it up a bit.

Right now, I've decided to level up the weirdest stats, but w/e.

The ones I've put the most work into:
Conjuration, Destruction, Sneak, Archery, Light Armor, Block, enchanting

Is this a good combination? I still find that I'm a terrible tank, and hate taking on multiple enemies at once. I think I've got the best light armour and shield I can find. I usually play with spell in one hand and shield in the other.
I tried doing a spell and sword combination at the beginning, but just felt too weak, and died easily.

Well anyway, give your opinion on how you've done mage/warrior hybrids. Might give me a few ideas.

If you've put something heavily into Destruction, one of the Wall spells does a nice job with multiple opponents. Think of combinations, too. Like casting Fire Storm, followed by Flame Cloak. You get Fire Storm's damage to start, followed by Flame Cloak's DoT plus your weapon damage at the same time.

I also agree that Conjuration is a nice thing to have, but I find myself using Conjure Storm Atronach almost exclusively. Just personal taste, of course.

Archery I don't find so useful, preferring ranged spells instead. Likewise with sneak. I reserve that for playing Assassin- or Thief-type roles, where backstabbing plays a major role.

Light Armor, along with the One-handed or Two-handed tree (depending on your weapon preference), are a must, IMHO. Remember that a Battlemage, like a Spellsword, is a combo class. So, if you can, you want to cover both sides of the combo as much as possible.

Yeah, I feel like I haven't been focusing on 1h enough, and it shows.
I actually find archery very useful though. When I'm sneaking up to somebody, I can usually 1 hit them with my damage multiplier. Much quicker than magic.
I'm just not sure if I should drop the shield, and go with 1h instead. What I've been doing is switching to mace when my magicka runs out, but my skill is kind of low.

what are the core skills?
I think you are mixing too many defencive skills in there, having block and light armor are more than enough defence, conjuration kinda breaks the point of having them you also hav two ranged skills coupled with sneak wich is yet another defencive skill that you cant use destruction with...

overall I think those skills dont synergize well with one another and will be overall ineffective/redundant.

if you are bound on sneak loose the armor and block, you can use archery and conjuration well with sneak and have both strong defence AND offence with those 3 skills as core alone, alchemy is a good support secondary skill there aswell so you can posion and debuff enemies with your poisoned arrows.

if you are bound on destruction drop sneak, archery and conjuration. light armor with block provides you a powerfull defence with strong mobility, destruction lays waste to enemies that are in groups and at range, and in short range when out of mana you can resort to a powerfull enchanted dagger/sword and poisons to finish it off.

I would suggest dropping Destruction. You don't need two ranged skills, because you won't be attacking with a spell and a bow at the same time. Destruction damage doesn't scale well, and doesn't get a sneak attack bonus, so I think you'll be better off with Archery. You should build up your Conjuration skill so you can have your minions tank for you; I suggest summoning a weapon and a minion at the start of every fight. I also recommend the Smithing skill, it goes a long way towards making your weapons and armor better.

What's the difference between a battlemage and a spellsword? My current character is an Altmer who's primary skills are conjuration, restoration, enchant, light armor, and one handed.

My Battlemage spec.

Main focus: Heavy armor, one handed, sneak, Conjuration, Destruction(at 50-70).
Never touched: alteration, 2 handed, or illusion.
The rest of the skills get occasional use and are at 30-50.

the perks are a secret

Thanks guys, I think I'm gonna drop destruction and block now.

I started off my character doing a type of damage dealing Spellsword class, but I felt very vulnerable. The walk from Whiterun to Winterhold was hell and it kind of turned me off the whole play style
After that, I decided to mix some tank elements in there too. Like you said, maybe I can level up my conjuration so the minions will tank for me.