Are thesee good specs for photoshop, illustrator, etc..No gaming

I can build a better system for bit more then the place is giving you. I would upgrade the ram to 4gb(2x2gb) Ddr3 1333mhz Dual Channel Kit and upgrade the video card to Nvidia Geforce Gt130 768mb Dvi Vga Hdmi its about $100 dollars more but its going to good for what you are going to use it

They'll be fine for what you need but I'd change a few things:

Get 4 gigs of RAM (2x2GB) instead. You'll be limited by 2GB and 3GB isn't dual channel.
Get a 7200rpm drive instead, such as the Western Digital Caviar Blue or the Seagate Barracuda. I have a couple of Caviar Blues and they've been great so far.
You probably don't need a dedicated graphics card, stick with the onboard graphics.
Get Windows 7 64-bit instead as 32-bit can only recognize up to 3.25GB of memory and the rest is wasted.
That PSU will certainly be one from an "no-brand" type of company which will be unreliable and probably will output nearer to 500W anyway; they don't often output as much power as actually advertised, upgrade to the Antec Basiq 500W, at the very least the 430W. With those you can be sure that they will be reliable and output as much as they say they will.
All of those parts are of course compatible.

As for better places to shop, I would HIGHLY recommend that you build one yourself. You'll get far better value for money and you'll be able to upgrade it in the future instead of having to buy a new computer. Most people in the US purchase parts from Newegg.com, it's a great website. I can give you a list of parts if you want to give you an idea but if you're definitely not up for building one yourself then I won't bother  
It's really not all that hard. Your first time will probably take you a few hours as you're being very careful and getting used to everything but there are plenty of guides on the 'net which can show you what to do and if you have any problems at all you can post them on the forums here.

thank you. and could you give me the list?
i would like to keep it below $500 maybe just a tad bit more.
but definatly not over $600 simply because i dont do any gaming.