How to remember variable values after rebooting an Arduino Uno R3 board?
The internal RAM of the Arduino will be reset when you repower the chip, so if you want to keep your data, you need to store it in EEPROM. 

If you are worried about the limited write/erase cycles, you should estimate how often the data would be updated (i.e. written to EEPROM) and how long you plan the lifetime of the device you build. If 100,000 cycles then still is an issue, you have several options: 


Keep the variables in RAM and only write them to EEPROM say every 5 minutes (100,000 cycles then makes about one year of continuous usage until the EEPROM might fail).
Use an external EEPROM (in a socket) that could be easily replaced if needed.
If replacing it is not an option, consider using an FRAM instead (advantage vs EEPROM: much more erase/write cycles but also very expensive, so not an option for large amounts of data but certainly for a few variables).


Note, however, that your description sounds like a typical use-case for user settings that you don't want to get lost on reboot. For those the internal EEPROM is the right place: only store them when they're changed and you're golden -- the user won't change them a 100,000 times easily...