If I provide a floor map, can Meraki tell me how many APs I need, and their locations?
You would need a survey done onsite. I can't speak for Meraki lol but it has to be done by either your tech team and/or other tech solution services.
I would certainly recommend a qualified professional examine your project. While an onsite survey is typically best, often with simple locations a predictive site survey can be quite accurate. An experienced professional should be able to look at your floor plans and with your network requirements determine if an onsite visit is required. At the very least, a predictive survey can give you an estimate for a BOM and cabling quotes. My advice is to look for someone who has ECSE certification or better.
You can try a predictive survey with this tool: https://rftool.cisco.com
Without knowing more about the environment the APs will be placed into, anything would best guessing. Is this an area that is already saturated with WiFi or is it a stand alone building with no neighboring buildings? Which band/bands do need to support?
If there is no established WiFi in the building I would suggest a site survey of some kind to assist with planning.
I'll confirm all of these replies so far. There are many variables and questions to be asked and answered, and might involve paid professional services to complete a more formal site survey. There are also tools that can assist if you have some of the expertise.
Cannot answer the question though except with a bunch of questions like is this greenfield or brownfield, what kind of venue is it, need to examine the floorplans and building materials, AP mounting & wiring options and location (like walls versus low or high ceilings), is the design for coverage or performance or some combination, what is the expected average versus max user density, what are the primary applications that will be running, does it need to support voice and/or location, what are the capabilities of the client devices (band, channel width, # streams, etc) among other things like what are your authentication mechanisms, are there specific performance criteria to design to, what are the plans to have different SSIDs for different use like internal vs guest, etc.
Sorry to ramble, there's a lot that goes into it, and the answer is always "it depends". PM me to discuss offline if you like.
I endorse @MerakiDave's comments and would add.
The requirement when designing a wireless network is to provide an acceptable level of accessibility, throughput and consistent reliability wherever users need wireless access.
This requirement is NOT well served by network designs which prioritise a minimal number of APs rather than meeting the requirement. Far better to have more APs operating at lower RX volumes than fewer powerful shouty APs.
At the end of the day, the success or otherwise of the network design will be assessed by the perceived performance by users.
https://www.ekahau.com/products/heatmapper/overview/
free version isnt the best but hook this up to a laptop, could possibly do it with built in antenna but id prolly buy a better one. you walk you click and each click will take a signal reading and eventually show you your coverage based on a floor plan you provide.