I have created lots of sites with similar functions, PayPal integration, User accounts, Interactive maps and Email notifications are my bread and butter :)
I have been through your requirements and summarised them below with some idea of time/cost for each item, obviously a lot of estimating at this early stage, I've also added a few things that you might want to consider to have the site work well for you and be easier to maintain.
My daily rate is £400 including VAT and the total is based on 17 days work.
- system administration tool (2 days)
> add locations
> add course time/day/number of spaces
> add trainers (name, email address)
> view history of transactions (courses booked, payments taken, etc)
- user facing booking system (2 days)
> select area
> browse courses with spaces available
> select a space on a course
> take payment with paypal and get users email address (not automatic with paypal so need to test that we have one)
> user and trainer notified by email
> mark course space booked
- Map customisation of Republic of Ireland (2 days, create artwork, create code)
- Requires log in for 'trainer' (2 days. Can they get password reminders? can you add/edit/delete trainers info from a 'master' account? )
- Paypal set up (1 day)
- Contact form / Email notification (2 day design and test (handle rejected email addresses, check for duplicates being sent, prevent abuse)
- 5-10 pages of website information (1 to 4 days depending on content volume!)