Programming other Atmel chips(excluding Atmega 328 and 168)
Since you say:


  Excluding the Atmega 328 and 168.


I'm going to assume that you already understand the general process for using your Nano as an ISP.

The Arduino IDE includes the Arduino AVR Boards hardware package which provides hardware definitions for specific configurations of:


ATmega328P
ATmega168
ATmega2560
ATmega1280
ATmega32U4
ATmega8


If your hardware matches the configuration of one of the Arduino AVR Boards then you only need to select that board from the Tools > Board menu.

It is also possible to program many other Atmel microcontrollers or alternative configurations of the microcontrollers included with the Arduino AVR Boards hardware package with your Nano but you will first need to install the 3rd party hardware package that contains the definitions for the part you want to program. You can find a fairly comprehensive list of these hardware packages here:

https://github.com/arduino/Arduino/wiki/Unofficial-list-of-3rd-party-boards-support-urls

Once you have found the hardware package that contains the necessary definitions you will need to install it. For this you have two options:

Boards Manager

The easiest installation option Boards Manager. Most Arduino hardware packages allow this type of installation (and certainly all of them on the above list):


Copy the Boards Manager package index URL.
File > Preferences > Additional Boards Manager URLs > paste URL > OK
Tools > Board > Boards Manager
Wait for downloads to complete.
Scroll down until you see the entry for the hardware package you want to install. Click on it.
Click "Install".
Wait for installation to finish.
Click "Close"


Manual Installation

Another option is to manually install the hardware package. For a simple package this would involve:


Download the hardware package
Copy the contents of the downloaded file to {sketchbook folder}/hardware. You can find the location of your sketchbook folder at File > Preferences > Sketchbook location.
Restart the Arduino IDE if it's running


After installation you will only need to select the correct board from the Tools > Boards menu. In some cases selecting a board may also add custom menu items to the Tools menu that can be used to adjust the configuration of the board (part, clock, BOD, etc.).


  using Arduino Nano as a Arduino ISP


Note that the correct term is Arduino as ISP. There is a programmer named ArduinoISP that is completely different from the Arduino as ISP. The confusion is increased by the sketch used on the Arduino as ISP being named ArduinoISP.