Given the huge number of journals around, it can be hard to even draw up a shortlist of possible journals for your research article. As well as talking to colleagues and investigating journals that you read and cite papers from, there are some tools that will help narrow down your search.
One initial strategy is to conduct a document search in Scopus or Web of Science using keywords and phrases from your own manuscript. The results of this search could give you an indication of the journals that publish research in your research areas. It is also worth looking that the literature that you are citing in your paper - where has previous research on this topic been published?
If you are looking only for open access journals, there are also ways of searching for these by filtering your search results in bibliographic databases and journal comparison tools. The Directory of Open Access Journals (DOAJ) is a useful tool for searching for fully open access journals.
When you've come up with a shortlist, don't forget to 'Think, Check, Submit' and to check out journal metrics and costs before you finally click on submit.
The JANE tool can help suggest a suitable journal for your paper based on the title and the abstract. The tool searches journals that are included in Medline, so is only really suitable for papers in this subject area. You can also use this to find possible reviewers for your manuscript if a journal is asking for suggestions.
There is a helpful FAQ section on the JANE website. The background to the development of the tool is explained in a paper by Schuemie and Kors (2008), DOI: 10.1093/bioinformatics/btn006.
If you are worried about disclosing the contents of your abstract, you can choose to scramble the text. You can also use keywords or just the title of your paper to conduct the search - the example below is with the text of the abstract scrambled.
The results page from a JANE search. Journals are ranked by confidence level and open access journals are clearly flagged. The article influence score from eigenfactor.org is also given.
The Springer journal suggester tool searches 2,500 Springer and BioMed Central journals to find a suitable match for your manuscript. You can specify an acceptance rate, impact factor threshold and maximum time to first decision to help narrow down your search. It is also possible only to choose fully open access journals. 
Screenshot from the Springer Journal Suggester: https://journalsuggester.springer.com/
JournalGuide is a free tool that was created by a group of former researchers and software developers at Research Square. The tool helps you to find suitable journals based on your title and abstract. You can also compare up to three journals at a time to see details of cost, publication speed and open access options. The tool uses SNIP values to calculate impact.
The search options using JournalGuide
Results example:
You can find the most suitable Elsevier journal for your research article by using the Elsevier Journal Finder site. Like some of the other journal suggesters, it will use the title and abstract of your paper and area of research to suggest suitable titles from the Elsevier journal list.
The list of suggestions will include information on journal impact, the acceptance rate, speed from submission to decision, speed from acceptance to publication, costs, open access options and embargo periods. You can sort the results on the degree of match with your paper, speed of publication, acceptance rate etc.
Screenshot from the Elsevier Journal Finder showing the information available. It is also possible to limit your search to only journals that have open access options.