I'm looking to put a decent set of speakers on the computer in the my bedroom. I'd prefer not to have a sub since I don't want it to disturb surrounding rooms (below.)

There are a few pretty good speakers you can go with! I am sure the neighbors with thank you for skipping on the sub, that is pretty annoying !  Just keep in mind "quality" does not always mean you have to spend an arm and a leg!
Amazon has a Cyber Acoustics speakers selling for $24.88!
specifics are:
Cyber Acoustics is the technology leader in affordable computer audio and speech recognition/voice interactive microphones and headsets. Its goal is to provide the consumer products that offer the most features, superior design, and performance for their money.PRODUCT FEATURES:Studio Series 2-piece speaker system;High excursion, efficient drivers provide extremely good clarity and greater dynamic range;Low distortion, high power amplifier technology;Bass reflex ported enclosure;Magnetically shielded satellite speakers;Convenient power on/off switch;Convenient desktop volume control;Headphone output jack;Power output 24 watts;3" high excursion dynamic driver;Power adapter include

Logitech is a pretty good and trustworthy brand in computer accessories!  There is a Logitech 980-000382 Speaker System which sells for $44.00! This one does have the sub, but really if you turn the bass down, it really wouldn't bee too bad!
specifics are:
Frequency response: 48 Hz-20 kHz (+/- 3dB) / Total RMS power: 25 watts (RMS) / Wired control pod / Room-filling sound & deeper bass / Sleek and stylish
With a convenient control pod and big, balanced sound, the Logitech's Speaker System Z313 is the easy way to kick back with your music. You've got power and volume in the palm of your hand with the wired control pod. Say good-bye to built-in Bass for all your PC entertainment. You can put this sleek system anywhere in your room; it complements your setup and your style.

There is another Logitech set of just speakers that is selling for $54.89, however, you will also get a mail in rebate certificate to send in for $15.00!
specifics are:
he V-20 Two Piece USB Computer Speaker System from Logitech offers good sound in a compact package. Operating independently of a soundcard, they plug directly into a USB port which also provides power. The speakers come with a protective travel case to let you easily carry them along with your notebook computer. These features and more make the speakers an excellent choice for mobile users who require high-quality sound in a small and portable package.

Travel Case

The included travel case lets you carry the speakers with you when you are on the road, making them an ideal companion for laptop computers.

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Portable Operation

The speakers are easily portable as they are powered by your computer's USB bus. No other external power source is needed, so you can use them anywhere you use your laptop.

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No Sound Card Required

Audio is transmitted digitally through the USB connection, eliminating the need for a soundcard in your computer and also giving you a pure digital signal to drive your speakers.

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Windows and Mac Support

The speakers will function on any USB

USB

USB stands for Universal Serial Bus. It is a standard connection interface that allows many different peripheral components such as printers, digital media players, external hard drives, and more to connect to a host computer. Some devices can also be recharged via USB connection. close

-equipped computer running Windows XP, 2000, 98SE or Me or higher. They also work with Mac computers running Mac OS X

Mac OS X

The operating system currently used by all Apple personal computers. OS X is based on UNIX programming code, and offers a high level of security. The operating system is also advertised as offering numerous user-friendly features and is ideal for those wishing to work with photos and videos. close

or higher.

Hey there!  After doing some research for you, I have found some really great speakers that have reviewed well.  Please take a look at the following.  Hope this works out for you.  Thank you for using imshopping.