I am 36 weeks pregnant after one successful IVF/ICSI cycle at ARGC. I attended the clinic during April and May so I can't recall every detail but hopefully the things I can remember will help you!
For the first appointment the doctor will go through your fertility history and will explain IVF process to you. I found it really helpful to do a lot of reading up on IVF before going to this - otherwise the terminology can be a bit baffling and it can help you can ask informed questions (my partner, having done no research, found himself a bit out of his depth).
One warning about this clinic is that although you will be given a specific appointment time - this means absolutely nothing! It always seemed to me that it was run on a first come first served basis. For example, if you arrive for an appointment at 11am, be prepared to wait until 1pm to be seen. However, if you turn up at 9am for your 11am appointment you will probably be seen at about 10am...
The monitored cycle just means that they will monitor you through one period with a few blood tests and scans so that they can assess your natural period and decide what fertility drugs you will need. From memory, I think there were about 2 blood tests and scans each at different points in your cycle. I really don't think you will need to stay in London for this.
Depending on how far away from London you live, you may find that it is easier to stay in London during your treatment. They really do monitor you closely at this clinic and you will find yourself queuing for blood tests at 8.30 on Sunday mornings (again, always get there as early as possible!). At one point I was going to the clinic for blood tests twice a day because I was at risk of OHSS, and after the egg removal (which is done under a general anaesthetic) I certainly wouldn't have felt up to long-distance travel. Once the eggs have been implanted the clinic will leave you alone for two weeks so there will be no need for you to be in London during this time.
I'm afraid I can't help you with places to stay in London as I'm a resident here: obviously the closer to the clinic the better but I would guess that hotel prices around that area are very pricey!
Although the organisation and queuing times at the clinic are shambolic, I really can't rate ARGC high enough. They really do look after you and you're monitored so closely that it isn't surprising they have such a high success rate.
I don't come onto this site very often anymore but please feel free to ask me any questions - I'm on firstname.lastname@example.org
The BEST of luck with your treatment!