Electronic – LED driver circuit with both analog and pwm control

For an "all-in-one" option, the ADB8810 looks pretty close to the kind of thing you want. If you search for "programmable current" on e.g. Analog Devices, Nat Semi, Linear Tech, TI, Maxim, etc you will probably find quite a few options like this.

Another option would be to use a DAC (or indeed a potentiometer if no uC involved) to control an opamp with transistor set up as a current source.

For ~1000 levels you would need 10 or more bits, so this would be pretty cheaply done.

Something like this circuit might do:

The transistor could be any NPN or MOSFET (with appropriate Vth) or darlington capable of sinking the necessary current (EDIT - as Wouter mentions the 2N2222 is not a good choice, something in a package rated for higher power e.g. a TO-220 package would be better)
Opamp should be rail to rail in/out if possible to make things easier.
The 1 ohm sense resistor can be changed to suit the current required. This was set up to output 1mA per 10mV in, so 3.5V produces 350mA (at the opamp input it is actually 1mA per 1mV, the resistor divider divides the DAC input by 10)

Here's another idea to add to the good suggestions proposed by others. If you're going to be using RGB LEDs, you should consider the power supply requirements of the device. The blue LEDs in the RGB LED package have a high forward voltage requirement, so you will pretty much need either a 3.6 volt lithium battery, or a 9 volt battery. The 3.6 volt battery is barely adequate for a blue LED - say you select your current limiting resistor based on this nominal voltage and the voltage decreases a few tenths of a volt as the battery discharges - the blue LEDs will rapidly lose brightness. You end up condemning your SO to carry around a 9 volt battery all night, or several 3.6 volt batteries in series, which is bulky.

The standard ATTiny is good to 10 mHz at down to 2.7 volts, and has two PWM channels and four AD converters. It will be slumming it just controlling a couple LEDs; there should be plenty of code space available to use the second PWM channel to implement a simple boost converter. The converter can take a barely adequate battery voltage and boost/regulate it to keep a blue LED's light output stable as the battery discharges. This opens up all sorts of possibilities for lightweight batteries; you could use 2 alkaline triple A's, for example, for really long life. There is another advantage to this scheme - you can dynamically modulate the LED power supply voltage depending upon which LEDs are being used. When the blue LEDs are on, pump the voltage up to what's needed to give them the required brightness. When they're off, drop the supply back to just above the battery output voltage for the red and green LEDS. This should give you significant power savings.

If you find that when using a 3 volt supply that the standard ATTiny browns out under some conditions when fed directly from the battery/batteries, you could try using the low voltage part, or you could actually set it up so that the direct battery voltage just gets it started, and then run the chip from the boosted supply.