Do you have a Homeowner's Association, or is this county property with no restrictions. Ditto to the above. Do you have no front yard, or no back yard? Seems like one part of your house has no property next to it... that would be the West side? Where are the windows? What is your view? Where is the street?

In general, landscape design looks at the clients' needs and wishes for the property as a whole and the creates a design that then meets as many of those as possible in the most pleasing way. Other than the sheds and the veggie garden, how do you want to use the yard? To my mind, that needs to be answered before any real plans are made. Is privacy (fence) more important than the veggies? Does it need to be there year round, or is privacy only really important in the summer when you will be outside more? Do you want a large open space for games or running around in the center? How much shade is there over the course of the day along the chain link or in other spots of the yard such as along the deck? Do you want a "pretty" yard or a kid-friendly yard or is the growing of food more of a priority or are they all of equal priority? Where will you be most likely to walk or drive and so will need to be left open? Where is water available, and would you be able to add hose bibs in other spots as needed? Do you want afternoon shade for the deck or other areas, and would you be more likely to plant a tree, or add a structure such as an arbor or shade sail? What other wishes do you have for the yard? As others have said, the more sun, the more successful the veggie and fruit beds will be, so too close to the sheds and the nearby solid fence which will provide shade should be avoided. You also will want to change your grouping/way of thinking about the plants from culinary to cultivation. Melons, like all your veggies, are annual plants, while most other "fruits" you have listed are perennials. The annuals and perennials each should have a planting area so that when clearing out and replanting annuals each year you aren't disturbing the perennial plants. The strawberries will need renewing every few years while each of the the shrubs and vines, which are fairly permanent, have different maintenance needs, and so should be planted in separate areas. If you grow herbs, some are annuals and some perennials. Consider overall goals and how else you will use your yard to help determine the best spot for the veggie beds. For instance, if you want the center of the yard left open, then think about putting your food plants along the chain link instead of a fence since it looks like it gets good sun. Or is the solid fence important enough the you should stockpile your soil for now or make temporary beds and then when the fence has been added, create the beds and plant food crops? Could you use the berry bushes and kiwi vines for your privacy instead of a solid fence? They are deciduous, so wouldn't be great for winter privacy. You would need to leave room between the shrubs and the chain link for accessing the vines. Fruit plants don't need as close access as herbs or veggies since fruit tends to be picked in chunks, while veggies tend to get harvested for particular meals, so think about putting the veggies and herbs closer to the house where there is easy access from the kitchen. Would you want veggies as a border around the deck, or does that either not fit the plants' needs or your wishes? So create a list of uses and priorities for the yard as a whole (swimming pool? play structure? bocce court? badminton net? trash can storage? etc, etc), prioritize them, and then start thinking about placement. You have already made one big decision, the shed size and placement, and so before making others, I would stop, step back and look at the yard overall. Take some time over the next growing season to look at sun and shade patterns (if you map sun as it changes from the vernal equinox until the summer solstice, you will have a good grasp on how it will look but in reverse for the rest of the growing season) as well as wind before planting anything permanent if successful cultivation of food crops is a priority. Once you have a good handle on growing conditions and your overall goals for the yard, then you will have a better idea of where is the ideal placement for each of the various uses you have for your yard.

Your backyard looks like my back yard did a half dozen years ago. Working it gradually, I selected the trees that were worth while, cut some out, and trimmed a lot. I also used a lot of poison ivy spray. With each opportunity I spent a half hour or so in the area with the first tool I saw from the list of tools mentioned above. In doing this I discovered that I had ground cedar, some wild lilies, and some other interesting plants. One of the first trips into the area I found a very young holly with about 6 leaves, I marked it and now it has a couple of dozen leaves and is about 13" high. I also found a beautiful young oak that I have been trimming and encouraging by heavily trimming the surrounding trees. One of the first things I did was take an axe into the area and cut every poison ivy vine I could find, yet taking care not to cut the Virginia creeper. I had been collecting all of the brush on a pile in the very back. My wife got a chipper shredder for me for my birthday, and now I my brush pile has become wood chip paths through the area. I also found that pine cones and gum balls make a good cover base for paths. One of the things we have is many different animals and birds in the area. Squirrels, rabbits, deer, and birds from humming birds to vultures, and dozens of different ones in between. You don't get that if you make your yard look like a golf course.

It seems to me that the umbrella lounge area is a bit far. If the round thing with something red in it is a water feature, I'd link it better to the umbrella area. I don't think I'd push the pair of chairs so far to the corner and then barricade them with a boulder that happens to dominate the center of that space. Better to move the boulder to nearer one side. Why the white stone circle around it? would be better coming straight out of the DG.