Arduino Underwater Inertial Navigation
The nano can run an IMU just fine, but unfortunately no accelerometer based IMU short of some fancy missile guidance tech is going to be able to track position as accurately as you seem to want. 

Since the Gyro and Magnometer only help with rotational orientation, the accelerometer is the only source of info on linear motion, and it has to be integrated twice to get position or distance. This site has a great explanation: 
http://www.chrobotics.com/library/accel-position-velocity 

As their table shows, even with an angular error of only .1 degrees, after 1 minute your position could be off by 62 meters with a standard quality accelerometer.

As far as IMU's go, the MPU 6050 (accl, gyro) and MPU 9150 (Accl, gyro and mag) are pretty standard in the hobby area, and sparkfun has some breakouts. The AltiIMU from Pololu has similar features and comparable cost. If you don't want to do the sensor processing the UM7 from chrobotics works well, but is significantly more expensive.