OK, further questions:
What supplies the USB power? You have not specified how much current the LEDs require so if these are high power types you will run into problems if the USB power comes from a computer USB socket. These are 'current limited' when first powered up and the device plugged in has to tell the computer the maximum it can demand from it before more current can be allowed. The problem with that is do be able to do that there has to be a full USB interface circuit and some 'intelligence' in your circuit to negotiate the amount of power it can ask for. This makes the circuit more complicated and WILL need a microcontroller with software. If the computer is switched off, you may also lose some or all the power of course.
If the USB power is coming from a wall adapter you might be in luck as these tend to be 'dumb' power supplies. Some, especially those designed to charge mobile devices may have a fixed power limit built into them though.
If at all possible, I would suggest you avoid USB as a power source and in view of the long periods the LEDs will be on, a mains AC power source would be a better solution by far.
The simplest design for what you want is a two transistor oscillator but these are very susceptible to variations in temperature and supply voltage, you may find the timing varies by as much as one hour or more between cycles. The other simple option is a tiny microcontroller configured as a timer. This may be as small as a 6-pin IC and it will give timing accurate to say +/- 20 seconds in 12 hours. They cost ~$0.50 US. All you need is one transistor and two resistors per LED so for a 5 LED system you would be looking at maybe $2.00 US and it would fit on a board much smaller than 4 x 4 inches.
Brian.