Lawn games hands down, we are doing that for our reception. Fun seating areas, tents in case it rains, music, snack bar, firepits if permitted incase it's cold. music, Twinkle lights or the Eddison bulb lights in the trees, like Christmas just white. Pinterest will bring you down the best rabbit hole for back yard ideas. Don't forget a dance floor.
First off, if you don't already have some large semi-closed in area that your guests will be able to move to if it's really windy or begins to rain, I would look into renting a large party tent as a backup. You can even simply set it up for the dinning area and have the sides open, so that it's easy to just roll them down if the weather takes a turn. It will also give you a roof that you can hang string lights, bunting banners and/or paper lanterns from. Depending on the size of your guest list, you might want to look into renting a port-a-potty or 2 as well so that people aren't fighting for the bathroom or continuously trotting through the house. But that's a know your crowd/size of guest list thing. Live music sounds so great for this style of reception, but i would double check with the by-laws for your town/neighborhood. A lot of residential areas have by-laws in regards to live music because it tends to be louder and less easy to control then a sound system. Shabby-chic and rustic decor usually suit these types of events. Don't expect to have a black-tie event in a backyard, and make sure people know to wear comfortable shoes.If you expect a lot of dancing, you might also want to look into renting a dance floor to avoid accidents.You can use picnic tables for dinner/dessert and/or bails of hay as previously stated.If you have trees around, you can tie streamers or long pieces of fabric to the branches to help decorate the natural ambiance. This can be used for your ceremony/arch and photobooth area as well and options are limitless. You can also hang pictures of either the 2 of you as kids on tree trunks or pictures of passed love ones.Lots of signage, lawn games and food bars/drink stations usually go hand-in-hand at backyard weddings as well. Also - depending what type of day/where your event is - if you can get a nice view of the sun setting, this is a great time to get your photo done.
Games, live music (maybe just a duo if you are concerned about noise), cute seating (benches, hay stack), agree with the lighting - twinkle/fairy lights would be so pretty, signage for when guests enter and bathroom sign, depending on layout of backyard I would figure out some way to keep it private physically/logistically in case neighbours are out in yard, could be a little awkward (unless they are invited).