https://www.pjrc.com/teensy/teensy31.html
Teensy 3.1 works with the Arduino IDE. However, the microcontroller is exponentially more capable. It has 64K RAM (instead of 2K), 256K EEPROM (instead of 32K), runs at up to 96MHz (instead of 16MHz), etc. Most of the device drivers for Arduino (displays, RGB LEDs, etc.) are also available on Teensy.
The only drawback is that it's not in the standard Arduino form factor, so it won't work with Arduino "shields" unless you wire each pin to where it's supposed to go (and the Teensy would need to have a compatible device driver, if it's something like a display or whatever). However, because of the faster MCU, and the fact that it has a DMA controller, it's been shown (with real world numbers) that a Teensy can draw graphics to an Arduino-compatible display several times faster than an Arduino can. If you care about your displays looking nice, and your users not saying to themselves, "This thing is so slow I can see it drawing every individual frame," the Teensy is a good way to get much better performance.
I started work on an Arduino-based clock a couple years ago, using the ATMega644 CPU (like Arduino but with 4K RAM, and runs at 20MHz) but it just killed me. I was
always running out of memory. I switched over to Teensy and continued my work, and I've never come anywhere close to running out of RAM. (Which is hardly surprising, since I have 16 times as much of it. Or 32 times, if we're talking about a regular Arduino.) The increased clock speed has allowed me to add all kinds of cool stuff, like a physics simulator and interchangeable pixel shaders that I can use to generate far more interesting effects. I would not be simulating physics or abstracting the graphics down to a shader level if I was still on a much, much slower Arduino. It just gives me so much more breathing room.
Another option would be Raspberry Pi. That
does come in a form factor designed for shields. It doesn't work with Arduino shields, but there are tons of Raspberry Pi-specific shields out there that do everything from drawing graphics to a display (including X-Windows!) to running a freespace gesture sensor. There are experimenter kits and you can program it in just about any language you want. (Arduino and Teensy are usually programmed using the Arduino IDE, which has a bunk old nonstandard C++ compiler with Arduino extensions that makes it act schizophrenic compared to a regular C++ compiler. You have to learn a lot of its vagaries.)