In my opinion, the most appropriate methods used to analyze the institutional urban planning of an urban agglomeration include methods that, in terms of key determinants, use the issue of achieving sustainable development goals, the principles of social environmental responsibility, eco-innovations in materials and construction technologies, environmental policy guidelines, etc., and meet safety standards. taking into account current and future projected climate changes.
An institutional analysis of urban planning is a useful and valuable tool in two ways: first, as a means (for example, analyzing the outcomes of multiple actors' planning actions); and second, as an end in itself (e.g. analyzing the actions of public sector organizations). In the first approach, we would use institutional frameworks of analysis to investigate the nature (e.g., source of institutional authority) and purpose (e.g., role within an institutional network) of the main institutional actors in order to explain the peculiar outcomes in urban planning.
The structure of institutions, which influences the pursuit of interests on the first level, emerges as a result of interaction between individuals or groups pursuing their interests. At both levels two and three, the analysis focuses on explaining the institutional structure rather than the impact of that structure on outputs.
If you say your subject country has insufficient or less institutional capacity for urban planning, then you already imply that it should strive for more - that there is some sort of benchmark, which we are missing. You could actually build more research questions (and papers) on this premise. One: you can compare, look for countries with varying approaches to urban planning and varying philosophies for urban governance, and do a comparative analysis with your subject country. I would personally take the UK - one that relies more on negotiations and flexibility with real estate market actors - and an EU continental (e.g. Germany) country - one that relies more on normative regulations. Maybe you could even split that into some country that focuses on prescriptive and another on performance standards - I think these neatly describe different institutional archetypes, at least for the industrialized west. Two: you can explore the implications of having a weaker institutional background, focusing on some key policy areas - like climate adaptation, as suggested by Dariusz. What should happen that does not happen because of weaker institutions? What are the symptoms that can be explained by it? Three: you can look into substitution of governance functionalities. Dissect what urban planning means and does, and investigate how this happens in your subject country? A stupid example: there are no zoning laws to determine building height, but whenever someone builds a new house, they negotiate with neighbours on where and how much shadow is appropriate. I would actually use Jakob Torfing and Eva Soerensen's typology of governance models (hierarchical, market, network) to identify local alternatives to traditional institutions. You can do this third paper in parallel with the second, in some cases, there will be a substitute, in others, there won't, and then there will be a negative (or mabye positive) impact. Four: if you are done, you can actually look follow a decentralization trend in environmental governance in Europe, and identify areas of planning, where you actually do not need more institutionalization, at least not in centralized, hierarchical structures. Eco-collectives, energy communities, community-based resource management are sound alternatives, and there are many more popping up everywhere. In many cases there are some digital technological solutions like platforms and blockchain that support them, in other cases there isn't. It is worthwhile to see, which planning instruments and capacities missing in your country could benefit from leapfrogging central institutional development, for a more network-based approach. The outcome of this research agenda would be sound recommendations for a governance model unique to your country, combining: locally existing alternative planning practices (paper three), new network governance institutions with planning capacities (paper four), and central institutions with planning capacities (in areas not covered by the previous two, and where paper two identified negative impacts). Publish these individual papers, and stitch them together into a diessertation, and you have a PhD. Let me know if you wish to collaborate.
The best methods are centered on non-architectural research, as design itself is a technique. Example of surveys? the CLASSIC right to the city by Henri Lefebvre (1968) that analyzes the conjuncture of cities, considering its own methods and providing a critical philosophical-sociological reflection, intuiting to propose a new way of thinking about urban space. This author even has a vast work that can help you.