Here is a great seed where you will be able to find both diamonds and gold only by digging some under spawn. It's a super good seed to use if you want to get your hands on some great tools just when starting out on a new adventure.
Once you've spawned continue by digging straight down. When you see your first gold ore there will be more than one gold ores there, actually a total of six gold ores. As soon you've mined those ores continue digging straight down.
After a while you will see some lava. Just jump up and place two cobblestone blocks underneath to block of the lava. As you start breaking the stones around you there will be more gold ores to be found.
To find the diamonds clear the area around you. Just make sure you don't fall into the lava as there will be much of that underneath you.
Seed: LBSG SEED