As for what to do in terms of designing or choosing a game, there have been some good suggestions already in this thread, but I feel you really do need to consider carefully how you spend this potential investment.
I know this might seem like a downer, but I would be very concerned about potentially being frivolous and wasting a good chunk of money. Its an exceedingly rare position you find yourself in and it would be far more responsible to invest the money at this point in time. You could then use any profit from such an investment to help fund your games later. There is really no reason to be in a rush to spend the money.
So honestly I would not take up her kind offer and invest it in 'designing' a game, instead I'd be asking her to help you invest it real-estate as she has done and shown to have a talent for, as on the face of it, that's the only way you are going to be able to make the money 'work for you'. In fact i'd wager you would stand a better chance making money from real-estate than counting on a success in the game market.
Though don't take this to mean that you should try making games, far from it. I would encourage you as much as possible to continue and follow you dream as programming/game designing can be very rewarding, just not necessarily financially ;)
The problem with making a game is that it has zero guarantee of making any money for you, more so as you don't appear to have a burning desire to create a specific project 'your dream game', hence your original post asking for suggestions. Indeed at the stage you are currently at, you really shouldn't need any funding at all to be developing some simple games, unless you really have zero free time due to educational and working to support yourself.
I think the concern I have with what you are asking is that you don't have a business idea to invest the money into that has a clear and reliable route to generating an income or experience for that matter. For example many business opportunities will usually involve buying stock, which could at least be sold at cost if the venture failed, but with software development the money is basically going on supporting you, along with maybe some hardware/software which will instantly lose value or is non-transferable.
These days there are plenty of opportunities and engines that will enable you to design and create games for almost nothing except you time and devotion. Far better to start with them and avoid the pressures of having to develop a game using some-one else's money. Indeed you'll probably have to create a few game projects before things fall into place and investing money on those would just be wasted. Then once you've hit on your 'perfect' game design and got it to alpha stage you can then use the financing to pay for asset production, invest in software or licenses you might need, put it into marketing, promotion and website creation, pay to enter greenlight ( I think they ended up charging to avoid spam projects didn't they?) etc, all the stuff that you simply can't do without money.
In short then, I'd definitely take up the offer of funding, but invest it, either in real-estate with the help of your cousin or some tax free savings. Then in the mean-time really focus on building a collection of simple games, working up to a cool project that you feel has a good chance of being successful. Use the collection of games as dry runs through the process of designing, making, promoting so that you build experience. You'll then be in a far better position to make better use of the funding which you could then take out of the investment.