By "L" shape do you mean that the garage would be behind the house with a side entry from the side street? If so, I think that would look great!

Some of it depends on the other houses around you and your neighbors. I always thought a corner house would look best with a driveway from the side to maximize the front yard and front elevation. However friends built a (very pretty) house on a corner and chose to have the garage and driveway at the front. In our neighborhood, this is where kids often play (basketball, etc.) and when we take walks around the block we often congregrate with people in their driveways, so it's nice to have it at front. Also if you have company or your kids are getting picked up by others, it's nice to have easy access from driveway to front door.

If the driveway is off to the side, depending on orientation and distance, it's more of a pain for guests or people picking up you / your kids to get to the front door. I love how a yard with no front driveway or garage looks, but I'd also think about how else you might use the driveway (b-ball hoop? kids on big wheels?) and whether you want to see the driveway from inside the house (e.g. when you're waiting for someone to pick you up.)

yes! the front of the house would face the street. the garage would be in back of the main part of the house. The shape would be like this: ______I

The other benefit would be it would "hide" the backyard from the side street and make a nice area for a patio. The kids issue- Maybe i could have another entrance from the front that would also go into the mudroom/garage area- that could help with the "kids" issue.

Mostly I am concerned about aesthetics/architecture.

I think you need to start with looking for floor plans of a similar style and find something that works for you. Many of the floor plan search engines have an option for what side of the house you want the garage, so that may be a good place to start.