@Rick Sheldon
Funny one here :) So, no idea if that was intentional - but it looks kind of like something wasn't quite fully planned somewhere along the way :)
A few things - some items, likely in your basement, still can exhaust through an existing chimney. Those would be your furnace and water heater. Check that first before you get too far. You'll see galvanized steel exhaust flue going into it down there, if it exists. If you need to upgrade to a HE furnace or a power vent water heater, in addition to what you're considering, that's more cost.
The other things that'll drive cost on this include: can your roof be patched? You'd likely want to remove the chimney above your roof line, too. How accessible is that?
Are you willing to do some work yourself?
The actual work to remove, is just labor. There's not a lot of material cost in all of this. You just need to cut and remove bricks. To patch the roof, you'll need some misc materials but it'll stay under probably $200 I bet. A bundle of shingles, some OSB, some roof felt, etc.