Custom cabinetry may be a great solution for you (and may cost the same or less than modifying). Call a local cabinet workshop and have them come out and measure and price a more modern cabinet built in!

Looks as though your cabinets are in great shape, maybe refacing them is an option?

Yes, you could paint the cabinets, although as another commenter mentioned, you may be able to replace them for about the same cost. I would definitely consider replacing the mirror with tiles. The ones shown in this photo are from Ann Sacks, but I would assume you could find some for a lesser price if cost is a concern.

Painting is an option but if you really want a contemporary look you will want a door that has concealed hinges which new cabinetry would give you. The door style with the flat panel actually is not a bad look. If you decide to paint them I would think about a taupe or grey and pick up the color in the granite. Picking out a unique granite with a flowing pattern rather than speckled can really make that piece a focal point. Another option is to go with tile like the other person suggested. If you went with a busy tile pattern you might want to think about an engineered stone counter top. They have a lot of new ones that are rather solid in appearance with a little movement which would show off the tile and not distract.

There are some great ideas in this pix that can be incorporated into your new design. https://www.houzz.com/photos/built-in-bars-phbr0lbl-bl~l_695?fi=144

Sorry, it's the 6th photo down.

Love those photos Michigan Mom and Karen Paul!

Thank you all for your great advice. Michigammemom, I love your pic. I might copy that style. One question for you, did you just cover the mirror with backer board, or did you have to remove mirror, fix the drywall and stick wall paper on new drywall? Please show me how to do it. Also, should I replace the glass shelves w. wood ones for a modern look? Thanks.

Karen Paul, I love and love that link. It gives me so many ideas which I can copy. Thank you so much.

Personally I like the glass backing & shelves.
I would add two doors on either end of the bar to enclose it using frosted glass & aluminium doors going all the way to the counter-top. I would then change the base cabinets to a high gloss wood grain or, for a pop of colour a high gloss red base cabinet with HanStone's Specchio White ~ Contempo CT402 counter. And yes, remove the tacky brass 80's sink ~ Have fun!

michellelove, the inspiration photo I posted is a gorgeous room designed by Martha O' Hara. It would be less destructive to put up a thin backer board over the glass, but depends on how far you wish to go with the renovation. I prefer the sparkle of the glass shelves.

Painting over the cabinets is certainly one option, it also depends whether it will work with the rest of your home.

https://www.houzz.com/photos/1512-dolphin-terrace-beach-style-entry-los-angeles-phvw-vp~235525

Thank you all for sharing your thoughts. I'm planing to pain the bottom cabinets in white to match with white kitchen, with inside hinges and add some knobs and handles, my floor will be wood in mahogany color. The wall will be painted with new lighter color (don't know which one yet, but something light to brighten up my dark wood floor).

I love the idea of creating wood shelving on top for display. Wetbars are out in my opinion.. Especially the mirrored back. Good luck! Michigammom's pic is perfect look.

We are purchasing an older house and will convert the wet bar into our new office area. An idea...