Generations 
I know some disagree, but, as I often repeat, I’ve not played a Gen Bb that I thought wasn’t nice to play, though they do vary from whistle to whistle. I think that is one that everyone should have on hand. I have a tweaked one I bought, and honestly I think I’d rather just buy three regular untweaked ones and play the best one of the three. The tweaked one is a good whistle, though. It is really a matter of taste, as far as that goes.
I’m ordering a Tilbury Bb, which is 75 bucks… have yet to see if that is any good. Sounded nice enough on a recording I heard, but of course that is different than having firsthand experience. Really, when you start getting into the lower keys it is more difficult to name good cheap options like it is with high whistles, as most of the Bb whistles I like cost more. It is worth checking with shops or makers to see if they have a return policy, that way you can try the whistles people mention without having to commit to anything more than the shipping cost, should you not like it.
That being said, the Syn Bb is not a bad whistle at all, and in your price range, and good if you like a more clear round sound (though I might add it doesn’t sound as “traditional” as a Gen, Sindt, etc. ). Plays nicely and easily, though, and Erle is good to deal with and might even be able to make one for you that matches how you’d like it to play. Mine is more sensitive (which isn’t bad), as I bought it in a set with Bb, B, C, and D bodies. The B and C bodies play and sound the most to my liking, but the Bb is also quite nice (The D has more oomph than I prefer, but that is to be expected when one head covers several keys.). I think he has come out with a larger bore set for the alto keys recently, so I am not sure if the availability of these has changed (or if the new set is better or worse). Worth looking into maybe, though.
The Dixon Trad in A isn’t bad, and I imagine the Bb is pretty similar (I think these are discontinued, but they are still easy to find). I don’t know about Dixon’s other Bb whistles, but the Trad in A is not hugely dissimilar to a Generation, generally speaking, but has a slight pinch of smokiness to the tone, and is a bit more free blowing. They are nice, though, and used ones would not be difficult to find. If you want to stay with something under 30, I can’t think of any other whistles besides Generation for that price, unless you buy used, aside from some hobbyist PVC whistles made by a variety of people. That’s another option- make one.
I really mainly just stick with Generation and Sindt for Bb whistles, though. Most Bb, A, and G whistles from “high end” makers end up having a “fat” tone and playability (such as Burkes), which I do not like as much in mid-range keys, as it makes it seem more like a low whistle to me when they are made that way, and I don’t think the pitch suits it, even though the same design may seem to work well for the high and low keys. I think these keys turn out best when they have a sound and playability more in line with the type of soprano whistles I lean towards.