I'm restarting my character and I'm going to try building a battlemage. A character who uses magic but can also use a single handed sword/bow. Would a Nord make a good choice. Or what race do you think would. In the past I have played mostly Breton's.

Actually, race has very little, and arguably any, relevance on viability of a given archetype.

Agreed, after bout level 6 any racial perks are kind of irrelevant imo. For a battle mage I usually go with a Breton or a Dunmer although the last one I played was actually an Altmer and went really well.

Incidently the battle mage in my avatar is a Dunmer and was one of my favourite characters of all time.

The Battlemage is the single most versatile and most variant of character made in all of TES. Everyone you talk to has their own take on what exactly a Battlemage is. One cannot look to previous installments and conclude it is what was listed within the presets. The developers themselves even chimed in to comment that those presets are nothing to be invested in.

There have been some very good Battlemage threads over the past couple of years. I'll try to find one and link it here.

EDIT :

Here is a good http://www.gamesas.com/topic/1450994-battlemage/#entry22413906 discussion to get some insight.

I like Orcs as battle mages. They are proven warriors, have Elven blood, and there are many Orc mages in TES history!

Dunmer and Argonians are other natural choices, although their skill set was more geared towards magic warriors in previous titles, not so much in Skyrim.

Personally, I would go spellsword! This would be my build: Light armor, Illusion, Conjuration, Restoration, One-Handed....always have a spell and sword in hand! Try dodging attacks and supporting with your magic schools. And add either Enchanting or Smithing on top of that. This is not so much a battle mage but I think it's cool.

For a Battle Mage how about Hvy Armour, Destruction, Restoration, Conjuration and 1H?