There's a popular rule of thumb that you should have 6 months income in savings. I'd like to see some statistics, because I doubt many people have anywhere near this much in savings. Personally, I keep about 2 weeks pay in my checking account. I have no savings account, but I have an investment account invested in very conservative mutual funds that I think of as my "savings". Right now I have a month's pay there but I usually keep about 2 months. I have another investment account that's more risky with 3 to 4 months income.
These days real estate is very difficult to predict. I wouldn't buy any sort of real estate as an investment per se. Buying a house or condo to live in, so that you don't have to pay rent forever, is a different thing. If you expect to live in it for at least several years that can be a good "investment". If you think that you can predict what will happen to housing prices in your area and want to put money down on that, feel free, but that's a fairly high-risk investment these days.
If you haven't maxed out your contributions to retirement funds, that's a good place to start. Especially if you get any sort of employer match. Lots of companies match 50% of employee contributions to a 401k up to some limit. If you're not taking full advantage of that, that's a 50% return in 1 day, you'd have a hard time beating that anywhere.
Obvious place to invest is the stock market. There are many choices of industries and individual companies to invest in. There are mutual funds and the like with a variety of risk levels.