When flying circuits under VFR, if there is no clear distinct checkpoint available, what can you do/use as a checkpoint? I suspect the runway but please correct me if I'm wrong. How do you make sure you don't converge, diverge from the runway or stray away from the centreline?
I'd like to add something to Ron's answer. Use of geographic checkpoints is used a lot in initial training but it can become a debilitating crutch that leaves you in the lurch as soon as you go to another airport. I teach in gliders where getting the circuit right is fairly critical the first time, there being only one chance to land.
The really important checkpoint or turnpoint is the turn from downwind to base. Learn to recognize the presentation of the runway when at a 45 degree aspect to it, which is normally the proper turn point for downwind-to-base unless you are extending or shortening your downwind for a specific reason. I always weaned my glider students from dependence on geographic points as soon as possible, and certainly before solo.
You are at 45 degrees to the runway when the extended line of the lengthwise edge and an extended line of the threshold are "even" relative to the horizon. This can be pretty tricky to discern at first but over time you'll learn to recognize this just by the appearance from your vantage point, and you will no longer care about ground landmarks.
I assume by checkpoints you mean visual cues for position. A "checkpoint" is different in the aviation world and is used by VFR pilots to report locations to controllers. These are denoted with a "Flag" on VFR maps.
The runway you are landing on is really all the visual reference you need. When flying a circuit you take off and follow centerline, which means you use the heading as a reference and add any cross-wind correction to stay on track. This takes some practice so don't be discouraged if you start drifting with the wind. Adding the appropriate cross-wind corrections directly after your wheels leave the ground is a skill, and then realizing that it changes about 50-100 feet above the ground is another skill.
300 feet below pattern altitude you should start your cross-wind turn. Usually by the time you get to pattern altitude it is almost time to turn downwind. The goal when you turn downwind is to be about 1/2 mile from the runway. In a 172 at pattern altitude, this means that the runway will cross your strut about half-way up (provided your seat is adjusted properly, this is important in flying patterns/landing).
The next "checkpoint" is mid-field downwind. This is when you start running your landing checklist. After that your next checkpoint is when the runway touchdown zone is about 45 degrees behind you, this is when you start your base turn and descent.
The last tricky turn doesn't really have a "checkpoint", the goal is to turn from base to final and roll out on extended centerline. You need to take into account if you have a tail wind or a head wind. For a tail wind you want to turn sooner, a head wind you'll turn later. Again this is a skill that comes with time. Extending your downwind can give you more time to correct any alignment errors. Starting your downwind too early will cause you to overcorrect or overshoot the turn.
After that your eyes should be focused on airspeed, altitude, and aiming point.
Really these are just a skill you develop as you train. Don't expect to be perfect in the first 20-30 landings/take-offs. Some pilots require hundred(s) to master the skill... Then they change aircraft and have to start again.