I'm doing my first PCB using Eagle and I'm struggling with the routing. I'm not good at layout type things so I'm relying on the auto-router. To get 100% routed I have to go with 10 mil traces and separation for signals and 16/10 for VCC and ground and set the routing grid at 4 or less. Even then I end up with dozens of vias and a jagged looking board. There's lots of room and I've moved a few things around but it's hard to see any improvement.
Are there any general approaches I could take to improving it? I did try hand-routing VCC and ground first but it just took me a long time to do and the result didn't seem any better.
The board holds an smd atmega328 with a power supply and ttl serial connections. There's a 74hc166 shift register and a 74hc02 glue chip connecting to a 30 pin connector which interfaces with an existing board.

In the board layout the power supply is top right, the atmega is below it, iscp beside it. the top chip near the 30 pin connector is the 74166 shift register and the 7402 is below that. I would like to leave the bottom part of the board clear although that's not critical except for the icsp and other connectors.

any pointers or tips gratefully accepted. Maybe for my next stab I'll try printing off the board and hand routing a chip at a time.