I have no direct experience of short language courses on the mainland however when I lived there I had several friends who gave favourable accounts of the courses they had undertaken. One of my friends spent a couple of months at 'Mandarin House' in Shanghai, while another spent a year at Tsinghua university in Beijing and yet another spent a year at the Harbin Institute of Technology.
While reports about all of the above were very positive, it was the Harbin Institute that got me thinking about possibly dropping out of work for a while and studying Chinese for a year or two. Being a northern school the local accent is reputed to be a very good standard putonghua, making the extra-curricula immersion experience all the more valuable. Courses there are also significantly less expensive than equivalent courses in Beijing, where prices are said to be quite absurdly over-inflated simply because it is the capital city and attracts the largest number of foreign students.
If you would prefer to study closer to HK, then there are so many language centres and universities that it can be hard to sort the good from the bad. While I was working in Guangzhou I heard good things about Jinan University, but almost every expat I knew there reported their disappointment in the various language training centres in the city (including Berlitz and New Concept Mandarin - both of which were described to me in the most unflattering terms).
One of the big issues, I think, is that different people want different things from their studies - they come into the class with different existing language levels and they want to learn or practise different things. Different students also learn in different ways. Some catch on to a language best through simple oral repitition; others benefit more when the approach is built around aural or visual teaching methods. Still others learn best simply by reading - pouring over rules of grammar and understanding the complexities of a language from written explanations. And the trouble is that unless you know which way is best for you, AND know the teaching methods of particular language centres, then landing in a class from which you will really benefit may be a bit of a hit-or-miss affair.
I normally recommend that people try free or 'taster' classes before joining any language school. Recommendations from others with direct experience is always useful as at the very least it can give you an idea of a school's character and the level of academic support that you can expect. Just bear in mind that a teaching style that suits one person might not be right for you. This is why two people, equally able in languages, can often have starkly different opinions of a school. If you're just going to the mainland for a brief couple of months' study, however, then you might not have the luxury of 'shopping around' (particularly if you will be applying for a study visa, sponsored by a specific university or language centre).
From the expats I have known on the mainland, private tutors seem to be better favoured as they can usually offer a course tailored to your specific goals and can fit lessons around your schedule. Really good tutors can also adapt their teaching style to give you the greatest possible benefit. Again, though, you often have to go through two or three tutors before you find one that suits your particular learning style and since you're looking to be on the mainland for a relatively short, fixed period then this might not be an ideal solution for you.
I'm sorry I can't give you any single, firm recommendation. I can't even give you a firm recommendation on whether to study in the north or the south, since while the local immersion in the north will doubtless be of greater benefit to your spoken mandarin, you might find that the proximity to HK that is offered by living in either Guangzhou or Shenzhen will be of use to you in preparing for your eventual move. What I can say is that when I have built-up enough money to comfortably take a couple of years off, I'm definitely heading to Harbin.