Bathrooms are usually one of the smallest spaces in a home, so it can be hard to make a big impact in such a tight spot. Between the toilet, sink and shower/tub there may not be room for anything else. So choosing things of the right size and scale is very important. The easiest updates are the things that you can switch out over and over again, and things that you can bring with you if you move (important for renters!) Shower curtains, bath mats and towels are the best examples that are not too expensive and can add a huge impact.
Pretty much every bathroom has either a towel bar or some type of hooks, so your towels are always on display and they might as well be pretty. If you are going to layer your towels I would stick to one size with a pattern and one size without. Or a curtain with a bold pattern and towels more subdued, this is a good trick to not overwhelm the small space with too much pattern. In a large bathroom a larger scale pattern on the curtain or bath towels would emphasize the space. Personally my bathroom is pretty small so my bath towels are a solid dark grey, and to add interest my hand towel hanging from a towel ring has a small grey and white pattern with a navy border. We only use this towel for drying clean hands to avoid staining it. I have an 'over the door' row of hooks that we keep two old hand towels on. Because honestly spotted/bleached towels drive me crazy. It really is a good idea to keep extra towels nearby (if not hanging right on the door maybe in a cabinet or basket) to keep your pretty towels on display clean and pretty.
If you have a shower curtain in your bathroom, updating that will make a huge difference, or even new window coverings. A bold patterned shower curtain can be the focal point of a bathroom, where a solid textured curtain will still add a lot of interest but may not be the focal point. Because my bathroom really doesn't have any interesting existing features (bold tile, fancy mirror, fun lighting etc.) I did decide to make the shower curtain the focal point. Mine is an older one from Urban Outfitters but I've put similar ones (above) that would also make a big impact. If you don't want your shower curtain to be the focal point choose more interesting bath towels or a unique bath mat.
Another easy update would be changing out the hardware. Depending on what hardware you already have this could make a very big impact. For example when I moved into my rental apartment the knobs on the bathroom cabinet were two different shades of brass, and every other fixture is pewter or chrome. So nothing matched at all! Because I am renting I decided not to change out much of the hardware as to limit the amount of holes in the walls. So I just swapped out the knobs on the cabinet using the same holes, (the not matching brass really drove me crazy) and I happened to find knobs at Pottery Barn for 99 cents a piece! Since they were such a bargain I didn't worry about matching any of the other silver finishes in the room and picked a burnished brass that I really liked. After switching the knobs I did make sure to put the old knobs together in a baggie and save them in my tool box. So when we move out the ugly mismatched ones will go back on and the pretty knobs will go with us to our new place.