I might need to overnight here (am still working on the Sheraton Brussels airport hotel)but I am wondering if there is a train line to the city near this hotel? Thanks.

Their website says there is a free shuttle to the airport, and I have read here that there is a train or metro from the airport to the city center.

If you have an early morning flight, then staying near the airport is a good idea (and you can't get closer than that Sheraton). If your flight isn't early morning, consider staying in a city hotel that is close to the metro/train station and head out from there.
Of the airport hotels, I think the NH Hotel (NH Brussels airport) is within a short walk of the Diegem train station (most of the airport hotels are in Diegem, but not all of them are within walking distance of the train station). Not all trains to/from the airport stop at Diegem (as I recall offhand), but many do. I know you can see the NH hotel from the Diegem train stop. The NH also has a shuttle, so you'd have two options for getting into town and to the airport.

If you opt to stay in the city and catch a train out to the airport, then your best bet is to stay by the Louise metro stop. From Louise, it's just a 3 minute metro ride to Midi, where you can pick up the airport express train. And it's a much nicer area than around Midi itself (or Nord, for that matter). There are several 4 star hotels near Louise offering excellent deals (around or under 100 euros per night). These include the NH Stephanie (rooms start at 69 euros per night but no airco, so I wouldn't recommend it for a summer stay), the NH City Centre (same price and I believe it has AC), the Sofitel Toison d'Or (about 110 euros per night, an excellent hotel), the Hilton Waterloo (same price as Sofitel), the Bristol (normally more expensive, but I have seen some 90 euro per night specials), and a few others.

Thanks BTilke for your other suggestions/options... I was hoping you would see the thread.

Thanks too Travelnut .

If you stay at the NH Stephanie, ask for a room on a higher floor. The street it's on slants, so some of the rooms on the first floor (second floor U.S.) are almost at street level, not best for security...esp. in warmer months when you'd be likely to have your windows open. Ask for 3rd floor (4th U.S.) and above.
P.S. Brussels NH hotels were renovated recently and their discounted rates are great value for money.