I am working on a VERY full featured alarm clock. It includes an Astrolabe and calculates sunrise, sunset, moon phase, and tides and other astronomical info. It stays in sync using a GPS receiver. It automatically handles daylight savings time. It talks using an MP3 module. It stores and announces 100 different holidays, birthdays, and anniversaries. The regular alarm only goes off on weekdays that are not official government/bank holidays, with separate alarms for a spouse, and different alarm times for weekends, one-off alarm times for certain holidays/anniversaries/birthdays. It does countdowns to Christmas and my birthday.
Well, it doesn't do all this stuff YET, but I'm getting there. I've got almost every aspect of it working individually, now I'm integrating it all together. The biggest problem I'm facing that I haven't solved yet is just how to display the huge trove of information it generates.
The Arduino is capable of all of this, so it shouldn't have any trouble doing what you are wanting to do. I hadn't thought of adding bluetooth and controlling it with my phone though. Hmmmmm, new feature! Bluetooth modules are available cheap enough and there are plenty of examples for using them with an Arduino. And Philips makes some LED bulbs that are controllable via bluetooth, with full fading and color control, so you could use one of them in your bedroom and have the Arduino clock control it.