I want to do a project where I gather data such as sunlight hours per day, as well as temperature highs/lows. Once I have gathered 24 hours worth of data, I want to hook it up to the computer to read off the values in Serial monitor. When I try and open the Serial monitor, it restarts the program wiping all the memory. I tried doing something with PROGMEM, but that didn't seem to help as it is only for constants. I want to avoid using an LCD to display data if possible.
Yes, this is perfectly possible. You will need to write a routine that you can trigger via Serial. For example you will listen on Serial until you get the
dump command. Then run a function that spits your variables out to Serial.
You just have to be careful where you save your 5 variables.
If stored in memory (RAM), you should avoid power loss. Therefore I'd suggest a FTDI USB-to-Serial adapter. There you just connect the TX, RX and GND wires and proceed with the Arduino IDE's Serial Monitor.
If stored in EEPROM, you can use the regular USB connector of Arduino.