Sofa tables: We built this island from two Hemnes Sofa Tables (ikea.com). They measure 61-3/4 inches long and 15-3/4 inches wide, making for a generous-size island. You can, of course, substitute a pair of smaller tables; just be sure they measure 28 to 31 inches tall so that after adding wheels and a countertop, you can achieve a comfortable working height of about 36 inches.
Casters: IMPORTANT! Be sure the casters are rated for supporting the weight of the completed island with top. We used 3-inch-diameter casters, though you could use 4-inch casters if you need the additional height for achieving a finished countertop height closer to 36 inches.
Lay both sofa tables upside down on a floor, then cleanly and squarely saw off the back legs flush with the tables' bottom frame pieces. To do so, use a square to mark the cut line on all four sides of each leg to be sawn. Then make the cut with a handsaw, using a sheet of thin and hard material -- such as plastic laminate -- to protect surrounding wood from the blade's teeth.
Note: If you find it hard to make the cut without scratching the surrounding wood, cut the legs a hair long and sand them flush with the bottom edge.
To strengthen and stiffen the assembled tables, sandwich a panel of MDF between the backs, cut to a width and length matching the height and length of the table backs. The ends (shorter edges) of the panel need to be straight and smooth, so use a straightedge and circular saw to make the cuts. Then smooth out any saw marks on that edge using 100-grit sandpaper and a sanding block. The block should be at least 12 inches long to maintain a straight and square edge (a scrap of 2x4 works well). Lightly round the edges of that same edge using sandpaper, matching the rounded edges on the legs.
Attach the MDF panel to one table back using 1-3/4-inch coarse-thread screws driven through the table's back frame pieces and into the MDF. For best results, drill countersunk pilot holes in the frame pieces, drilling from the inside of the table cubbies. One screw every 10 inches or so will do the trick. Use the same method to align and attach that assembly to the other table. Set the full base assembly upside up on a flat floor to check that all four legs make contact with the floor. You might need to cut a bit of wood off one leg to fix any rocking.
Turn the base assembly upside down and mark the centers of each leg bottom by drawing intersecting diagonal lines between the corners. At each marked center, drill a hole sized for accepting the caster socket, then gently tap a socket into each hole. For now, do not place the caster stems into the sockets.
Prior to applying primer and paint, sand all exposed surfaces (including the cubbies) with 150-grit sandpaper. Then apply a good-quality latex primer. The exposed MDF edges will greedily soak up the primer, so apply two coats to those areas, sanding gently between coats to knock down any raised MDF fibers. Then apply two top coats of paint. Allow the paint to dry and harden fully before handling. Two days at 70 degrees F and average humidity should be sufficient. (Follow recommendations on the paint can.)
Build your own countertop or have one fabricated at a cabinet or countertop shop. Because we chose a quartz-surfacing material requiring specialized cutting and joining tools and supplies, we had the work done by a professional fabricator. Though the Samsung material is only 1/2 inch thick, we had our fabricator build on and around a slab of two layers of laminated ¾-inch ultralight MDF to create a top that appears to be a 2-inch-thick slab of quartz. That thickness gives the top visual heft and made the surface that much closer to the optimal finished height of 36 inches. Working inside the upper cubbies, attach the top by driving 1-1/2-inch coarse-thread screws through the sofa-table tops and into the countertop. Like before, drill countersunk pilot holes for those screws.
Outfit the cubbies with storage options (see below), and attach the casters.
Left to Right: Use tension curtain rods to create dividers for cookie sheets, trays, and cutting boards. Mount closet-rod brackets inside an open island cubby and insert a dowel to hold a roll of towels. Thread dowels through the open holes of a plastic basket to keep stacks of paper plates and napkins upright. You can't go wrong with labeled baskets -- group like items together to make baking a breeze.