It would be significantly less expensive and use significantly less energy to have one unit do the job. Ice makers are noisy energy hogs. They don't "keep" ice. They just make it. Continually. Which means that if you don't use the whatever 60 pounds of ice a day that it makes that it just melts away and has to be drained. You are paying for all of that energy to freeze all that water and paying for a pump to pump it all away unused. (Unless you plumb in a gravity drain.) And they aren't happy about being turned off and only turned on when there's a party and you need a bunch of ice. It's a bit less convenient to go and buy a bunch of bagged ice for parties, but you can buy a heck of a lot of ice fore $2500+ that is the startup costs. Running costs can be from $20-$50 a month depending on model. Most refrigerators, even if they aren't Energy Star, will only cost you around $55 a year to run. "Beverage fridges" aren't generally that energy efficient. Nor are they that cold. They don't have freezer sections either. They start at about $1200 and go up from there. So, you'd have a $3700 beginning expense if you went with a beverage fridge and ice maker and you'd still have no freezer to chill down the Jello shooters or keep Popsicles for the kids. Depending on how much traffic this bar area gets, you might even want to go for a 30" or 33" fridge rather than a 24" one. Choosing stainless would be less than choosing a paneled one, but that's an aesthetic decision as well as a monetary one.

Excellent questions above .... 1)Would you still use it as a bar for entertaining? The cabinets could be repainted and new long modern handles installed on the doors. Then replace the countertop to suit your new decor -- and switch the sink/faucet to chrome or silver. Consider adding a bar fridge inside the cabinets .... OR if there is enough floor space -- add a counter bar and stools in front of the unit. 2)How about as a bookshelf/closed storage unit? Cap off the plumbing, remove the sink/faucet/replace the countertop. Remove the glass shelves and mirror. Add new wood shelves and backboard. Paint the whole unit to match the new decor. Add modern handles to doors. 3)Perhaps you need more closet space? Pull out the entire unit. Cap off the plumbing. Add custom closet inserts for extra hanging space for coats ... and other out-of-season clothes/shoes/boots. Add closet doors. Paint out to match decor. 4)Need more display space for a large artwork? Pull out the entire unit and cap off the plumbing. Remove the shelves and the mirror. Add a large artwork and a console table/cabinet below it. Just some thoughts ....

Bathroom vanities aren't that deep, usually about 21 inches. Kitchen cabinets are deeper, about 25 inches. Do you want it to be closer to 27 inches deep? Home Depot and Lowes have base kitchen cabinets in "unfinished beech". They come in multiple sizes, some for a sink, some with drawers so you can mix and match and they are ready to be stained or painted any color. They're about $80-$110 depending on the size and if it has drawers.

Your inspo pic looks more decorative than functional. Wine should not be stored at room temp nor exposed to light. I would opt for less display space for knick knacks and more shelves for booze and glassware.