Dear Frank,
The answer is YES and NO.
The last time l checked USD to GHc exchange rate was over 1:3 therefore USD1,300 should get you a little over GHc3,900.
1) 2 star hotel (bed & breakfast) - between GHc40 and GHc100 per night. A five star hotel could cost in excess of GHc500 per night. If you intend to live for much longer then you may want to rent a small flat, most landlord would demand a few months/years advance rent payment but would work out cheaper than a B&B.
2) Food - lunch or dinner from top hotels could cost between GHc50 and GHc80. However, some good but inexpensive restaurants like Papaye would cost less than GHc15. However be very careful of local food sellers by the roadside, not hygienic and definitely to be avoided. It would be a lot cheaper to cook if you have access to a kitchen
3) Travel - there are no meters in taxi's and most drivers tend to inflate prices if your look or sound foreign. You would need a trusted local resident to guide you. Minibuses called "trotro" are cheaper but most of the cars are not road worthy and might be infested with pick pockets and petty thieves.
In summary, if you have a trusted local guide then YES, you should get by on your budget. However, if you are a stranger to Ghana with no local links then l doubts it.