If you're gonna go to 'bago, that's where you're going to end up. Getting to the other lakes isn't going to be as nice from Winnebago as the visit would be if you were to drop in somewhere in Oshkosh. Closer access to the rest of the lakes, plenty of places to eat nearby, and super close to the freeway for anyone coming. Butte des Morts to Winneconne to Poygan, up the Wolf to Partridge, all of that is a nice trip, buoys are well marked for much of the area, and the water will be super nice. I'm biased because I'm ON Poygan, but that's where I'd consider.
As for the algae blooms, there's no rhyme or reason, as the "season" for them is mid June through September. The deciding factor on them is the weather. Extended periods of warm weather and calm days will bring them on. As for the green that might add some color to your boat, it's more of the water in general, and not really the algae. Yes, it'll contribute, but because it's all relatively shallow, you'll get a lot more stirred up, as well as a lot of "help" from the duck/goose population. In the creek by us, the phrase is "it's only about 2 feet of water and 5 feet of loon shit". Poygan itself used to be a wild rice field, which is why my family came to the area - the waterfowl and the hunting action. That kind of depth is not going to get you crystal blue water LOL
The chain over by Waupaca/King is VERY nice for a trip, but IMO, it's a waste if you go there thinking you'll enjoy "boating". There's a ridiculously small area that you can actually open up the throttles, and other than that, it's really almost entirely slow/no wake. There's 2-3 bars to go hopping around at, and as a result, they're generally swamped. It really is more suited to pontoons, fishing, and canoes/kayaks. The "booze cruise" they have is really fun, but more of an adult thing, and it's on the "paddlewheel" they have there, and you'd have to find out when they're going out.
If you're coming to Poygan, head over to Norwegian Bay by Indian Point. There's ALWAYS a group there if the weather is nice enough, and the water will range from 1.5-4' over quite a large area - right in front of my own place, for example, you can walk out at least a hundred yards before it starts to get deeper than 3'. My own launch can only handle legit parking for a few boats, but if a group is coming, I can easily secure parking for 15+ boats with the neighbors - we just don't advertise for strangers ? Alder Creek is where our launch is, and anyone new to their boat is welcome to come and enjoy the nice low pressure of the area (as long as duck/goose season isn't open, then we're friggen Newark airport for boats!)
There's 2 bars to easily access from Poygan, Captain's Cove and Boom Bay Bar & Grille. Both are...worth the visit for their "unique" atmosphere. A good attitude is necessary, because the customer is NOT always right LOL Heading up the river (Wolf) from Poygan, it'll be slow/no-wake for chunks, but if you get too hot, you can stop at Wolf River Lodge, Hahn-a-Lula, Gala Resort...if you're getting low on fuel, Anchor Point Marina will get you where you need to go...little further up the river, "downtown" Fremont will have The Bridge Bar & Hotel Fremont right on the water (both likely to be SUPER busy if the weather's nice. A little further up the river is The Nauti Turtle, and if you've made it that far, you can see the hook on Partridge Lake where there will also be a nice gathering of people if the weather is nice.
If you stop on by, make sure to wave with all five fingers, and I have friends and relatives spying all over the place for me, so if you sink your boat, there's a good chance I'll not only hear about it, but someone will have video to pass along to me!
I'm not sure if the Sand Bar Bash is going to happen again this year, but if so, that's on Butte Des Morts sometime in August. If you're interested, look up their facebook page. I'm not on Facebook, but the neighbors usually let us know when it's happening. That's not really as conducive for a meetup, since there's a few hundred other folks there, but it could easily be arranged - just something to consider if that's a timeframe being mulled over. My boat is somewhere in this pic for an idea of how many will be there for that: