You should never worry about looking cheap when informing the sommelier of the price range you’re comfortable with for purchasing a bottle of wine, especially if the wine list includes bottles within that range. Taking an initial look at the list before notifying the somm or server will give you the best idea and there’s no reason to be nervous doing so.
If a bottle is on the list, it’s there because the person who built the list is excited about the bottle and wants someone to buy it. So you don’t need to worry if the bottle you’re interested in purchasing happens to be on the lower end price-wise. It’s very possible there is a wine in the range you’re looking for that is an incredible value that you will absolutely love, so trust the staff.
The best way to let the sommelier know what you want to spend is by either saying your price range out loud or by pointing to a few bottles on the list and noting you’re looking for a bottle that is around those price points. What you want to avoid is simply asking the wine professional for a bottle they are excited about right now, or for their best Pinot Noir. Doing this is a bit like playing Russian roulette; you might be recommended a bottle that is squarely in your price range, but it’s also entirely possible that the bottle will be in a range that is more than you want to spend.
Declaring your price range at the beginning of the conversation will ensure you get a bottle you are happy with, and won’t leave you feeling uncomfortable about turning down a bottle that was recommended due to the price being out of your comfort zone.