I have a Bose speaker system for my PC. It is a 3 piece system consisting of a box and 2 smaller speakers with plug for head phones. I purchased an all-in-one PC where there is no place for a plug-in. Are there wireless speakers of this caliber?

Are you sure your all-in-one doesn't have the right connections? Normally all you need is a headphone jack. Otherwise, you can get USB sound devices that will allow you to hook up speakers to them. I would take a picture of the ports on the back of your computer and take it to the store and explain what you are trying to do. Otherwise, you will probably need to look at Bluetooth or USB wireless speakers

Any bluetooth speaker system will work.

Bluetooth or USB will work or could even do an adapter from USB to 3.5 mm or a bluetooth reciever hooked to the old system. However there is a downgrade on quality when using bluetooth. It's generally very good but if you're playing high quality audio on good speakers you can notice a difference. As noted though it is very unusual to not have a headphone jack/3.5mm connection though.