Whats a good mini/travel amp that has decent distortion? I curently can't have all my regular amp/effects out due to not having a room to leave them out due to my dog, so I was wanting to buy a small amp that had distortion on it that I could easily put up every day till I buy a house and have a room dedicated to my guitar stuff.
If you don't mind playing through headphones/external speakers, try a Vox Amplug. There's a few different flavours, some with FX like delay and whatnot. I've owned a couple, love 'em to death, and if the gain alone isn't enough you can always hook it into a pedal.

Similar to that Vox, but pricier and more powerful, are portable digital modeling devices like one of these (some are discontinued, can still be easily found):

Boss Micro-BR 4 track

Boss Micro-BR 80

Pocket POD

Tascam GT-R1

Korg Pandora Mini

Korg Px4

Korg Pandora Stomp

Korg Px5

Here is a visual comparison of (left to right) Tascam, my PX-5 and one of my Px4s to my old Aiwa cassette player:

Only the Tascam has decent acoustic recording capacity. All DO have features like tuners, metronomes, drum synthesizers, and digital amp & pedal modeling.

So with decent headphones, you can rock out like you were playing Texas Stadium. And yes, they are all about the size of an old Walkman.

The ones I own: the Tascam has the external mics, a phrase trainer (loop & slow down stuff for practicing), and takes SD cards. Both it and the PX5 can connect directly to your computer via a USB port. It is less powerful than the PX5, but, oddly, the PX5 does not have a belt/strap hook.

The ones I don't own: The Line6 PocketPOD is, I believe, the most popular device like this; the Boss might be the most powerful (and priciest); the Pandora Mini is the smallest (its about the size of a stack of business cards), cheapest, and least powerful.
Yamaha THR is perfect. Will be the best portable tone you'll get.
They make a few different models, so no matter what you will be playing theres one for you.
They come with Cubase (pretty sure) and make awesome tools for recoding quick demos and stuff too.