Depending on how many LEDs you're talking about the current draw will be accumulative, so 4 LEDs rated at 20mA each would be an 80mA load, 4 x 20 = 80, so whatever you're using would need to be able to source that much current.
That DC-DC setup there would work, after you have the correct values for everything, but it's going to take up some room unless you go with all SMT components to build it. On a side note for that schematic, you'd want the EN pin connected to a switch or some switched voltage source, otherwise the thing will run all the time and the LEDs would always be on. You could look into Charge Pumps, they only need a few Caps to work and for powering LEDs would be fine after it's all setup.
They also make LED drivers, and one of those might work for what you're after.
Linear Technology has all of these things -
http://www.linear.com/" onclick="window.open(this.href);return false; and a pretty good site for going thru all of the options and such each one has.