The fact that Rovers sound as good as they do for the money they cost is reason to recommend them as a good beginners banjo, but they don't make banjo ukes that I am aware of.
Eddie Finn and Morgan Monroe are decent new instruments. I've enjoyed playing Lanikai and even the big Gold Tone, though the smaller Gold Tone banjolele I played wasn't my cup of tea. I like the Firefly and really like the Mainland.
However, I'm with Ben and Dave, though - Vintage is what I prefer. Three reasons:
Value: A Slingerland Model 20 in great shape can be gotten for less than $175, and a model 24 in excellent condition can be gotten for less than $250. Stromberg-Voisinetts can be found ranging from $150 to $300 in excellent condition, price varying depending upon the model A Gibson UB1 or UB2 can be found on Ebay for $350-600. Compare those prices for Gibsons with comparable prices for new ukes that I don't think are near as good. I don't know why you wouldn't pick up a perfectly made 75 to 85 year-old Gibson for the same price you would pay for a new Lanikai. A new Bean Sprout is in the $1k to $1,500 range. An old Ludwig Wendell hall in excellent condition is in the same range. They're very different instruments, the bean sprout is a great piece of workmanship, but they are comparably priced, so you can afford even the best vintage instruments when you look at the prices for the best new instruments. And - Langes, Weymanns, and Stellas/Schmidts in good to very good condition ($50-$200) are much cheaper than the cheapest of new instruments.
Feel: New banjo ukes have a wider and thicker neck. This is fine - it's what ukulele players want and are used to. But, vintage BUs have narrower, often V-shaped neck. THere's a reason for this; the style of play in the 20s and 30s was faster with more jazz changes, and the tenor-banjo style neck allows that style of playing. This is how I like to play, and I find the feel of the new BU necks too much like a wooden ukulele neck to suit my style. It's a matter of personal preference.
Sound: well, this is highly subjective, as even individual examples of the same BU sound totally different. Let's just say that I prefer the vellum and goat skin heads to synthetic, and I enjoy adjusting tailpiece, nut, neck via coordinator rod and dowel, and bridge height to get the sound I want. The fact is, if you buy new, you are not getting an instrument that works out of the box. You're going to be getting into adjusting and modifying slightly eventually, and you'll see that you don't just buy a new BU and expect you're not going to tinker with it. You will eventually if you are at all sensitive to the sound you're making and want to make.
The person who wants a banjo uke that needs no adjustment reminds me of the joke the David Johannsen told once when he was on stage and strummed an old Martin 00-17 guitar at the top of his act to find that it had gone wildly sour. "I don't understand," he growled. "It was in tune when I bought it."
It might be set up when you buy it, but you will eventually change the set up.