I'd suggest getting a multi-ticket (can't remember the real name, but you get a number of rides on one sheet and you just fill out one line for each trip) while you're in Belgium for the train! The train is pretty cheap (at least certainly compared to the UK!), and most of the main spots are around an hour away from Brussels by train! I lived literally 5 seconds outside of Gare du Midi and many times me and my housemates would all be having our morning coffee on the weekends and randomly decide to hop on the train for a quick day trip. We would buy these multi-tickets and just share it, and normally that'd cover all of us for there and back and we saved so much money rather than each buying our own tickets individually.
If you want to see as much as possible, you can do most of the destination cities in Belgium in a day. Of course, they certainly could (and should) take longer than that, but mostly they're good for just wandering anyways so I think it should be a fine first trip, and then if you wind up moving there you can follow up more thorough visits! Brugges is certainly just a day, Ghent is just a day (though I will say it's so lovely you'll never want to leave!), Leuven is really just a day. Antwerp is maybe two (I visited twice and don't feel like I saw everything, but to be fair once was Pride so we wandered through town and ate free ice cream but didn't truly explore besides bars and then we were already very drunk, and the second time it snowed and we were not having it so we left way early), Brussels is huge so you'll just have to make your priorities. I know they offer a tourists discount if you want to see a bunch of sites, but it's not worth it. I didn't make it to Liege or any of the others I haven't listed, as we sort of fell into the trap of loving Ghent too much and returning rather than going new places! You can also take the train within Brussels and they almost never control within the city (and if you go with the multi-pass and you see them coming you can just jot it down real quick anyways). Otherwise, all public transport is on the same system which is nice (ie the same pass works for buses, trams, metros), but it's moderate/high priced not cheap so I'd just hop the train and walk.
I second finding local eateries, food can be expensive if you go to the wrong places. I can suggest a great african place in Saint-Gilles if you're interested, or if you want to go the grocery route I 100% suggest the Saint-Gilles market sunday mornings- I fed myself for less than €10 every week doing that, including incense but excluding coffee
I know other neighbourhoods have cheap markets too, but watch out because some like Ixelles (in fact avoid Ixelles altogether it's sooo pricey! except knees to chin which is good for lunch, and the mangoes at their market are cheap too) are way more expensive than a grocery store would be. From what I could tell the main grocery stores have comparable prices, but make sure you're going to the real store and not the quickie version. Proxy Delhaize isn't too bad, but the Carrefour Express will gouge you. Lidls suck in Bxl, but of course they'll be cheaper so it's your choice.
There's a number of free things to see in Brussels as well if you want, and I think it's the first Wednesday of the month museums are free or cheap or something (I'd google it to be sure). I can't speak for normal museum prices, because I always paid the "art" student discount. Outside of that I think I have a list from when my friends came to visit me that I could pass on with some free things to do if you wanted. Bars aren't super cheap, I'd suggest buying beers from the grocery store and going somewhere public (Flagey/Palais du Justice/the canalside in Ghent) if saving money is #1 top priority, but I do suggest going to a bar while in Brussels as it is a big part of culture. Our go-to was Maison de Peuple. To be fair, I don't think they're quite so expensive if you're not me, since I hate beer so I exclusively drink kriek (cherry beer)
- which, btw, I suggest trying while you're there. Prices do vary widely at bars though, so watch out.
All my trips to France were long ago and expensive, so I'm no help there, sorry! I'm jealous if you wind up going, I miss BE more than anything!
EDIT: I just re-read you original post. Be careful about downloading maps, I've never gotten it (it being Google Maps) to really work. I think the problem is that it only downloads
driving directions, which isn't super helpful.