$500 is a drop in the ocean, if you want some small speakers for playing with your pc then i think you are asking the wrong people. You have not given any idea of your use, ie critical musical listening/gaming/production. Whether you intend to listen only in the chair directly in front or you want a room filling sound. People here are both generous with their opinions and very knowledgable and are not giving you bad advice.
If you dont want a sub then you really need a minimum of 5.5" drivers in a 2.0 (2x speakers, 0 sub) so that gives you an idea of the size of speaker you are talking about. The width of the front panel is going to be minimum of 6" and probably deeper than they are wide. So the question you need to ask yourself is how much space do you have either side of your monitor on your desk, assuming its a pc based music set-up.
This moves us on to connectivity, do you plan to run these with the tiny headphone jack coming out of a laptop? A dedicated PC soundcard? An external Device with TRS/XLR ability?
I am trying to be completely helpful here, we need to know exactly what space you have, your existing equipment and what you plan to use it for. For example I do some home producing (making my own ****ty music) and have my PC hooked up via usb to an external audio interface (soundcard) with allows me to connect all my instruments and feed my speakers. I use a set of Adam A7X speakers which are BIG and self amplified. Just the soundcard and speakers comes in at about $2000, and yes its way more than you need for listening to tunes on spotify but I am just trying to clarify your needs before we start narrowing down what to advise.
TMRaven, CEL4145 and RonaldDumsfeld are proven posters on this site and would not troll you for fun. They are all offering you very broad advice because without specifics thats all they can do.
So give us an idea of your source (pc and soundcard) what space is available on the desk (width/depth each side of the screen) and what you are trying to achieve (personal listening at the desk vs room filling) and I am sure you will be given lots of options to research further.